{
    "connections": [
        {
            "in_id": "{2b636439-53b4-4770-9251-056d340a8ebc}",
            "in_index": 0,
            "out_id": "{8dc7f721-0eef-4297-afa9-4a75f06eccad}",
            "out_index": 0
        },
        {
            "in_id": "{1b85d168-4f3a-4108-9d1d-b827b3647a4d}",
            "in_index": 0,
            "out_id": "{8dc7f721-0eef-4297-afa9-4a75f06eccad}",
            "out_index": 0
        },
        {
            "in_id": "{698b0166-82c2-451b-bcfe-62471c87e672}",
            "in_index": 0,
            "out_id": "{8dc7f721-0eef-4297-afa9-4a75f06eccad}",
            "out_index": 0
        },
        {
            "in_id": "{a1ae2f7e-396d-42f8-b98c-9858cea1cbe8}",
            "in_index": 0,
            "out_id": "{8dc7f721-0eef-4297-afa9-4a75f06eccad}",
            "out_index": 0
        },
        {
            "in_id": "{90dd300d-b6ad-4556-b4dd-701b7ace24e8}",
            "in_index": 0,
            "out_id": "{8dc7f721-0eef-4297-afa9-4a75f06eccad}",
            "out_index": 0
        },
        {
            "in_id": "{77ff52dd-2b6f-481e-a280-7f2b81da90b9}",
            "in_index": 0,
            "out_id": "{26d21317-2ba9-4e38-b176-683f881cf577}",
            "out_index": 0
        },
        {
            "in_id": "{bd2aaee5-528a-4c92-a8fe-907e22dd5ff3}",
            "in_index": 1,
            "out_id": "{4b4b0934-8da5-4485-8537-29496c8756d5}",
            "out_index": 0
        },
        {
            "in_id": "{e672ea0c-a142-44ab-883f-aef3b16086ed}",
            "in_index": 1,
            "out_id": "{77ff52dd-2b6f-481e-a280-7f2b81da90b9}",
            "out_index": 0
        },
        {
            "in_id": "{4b4b0934-8da5-4485-8537-29496c8756d5}",
            "in_index": 1,
            "out_id": "{fe1bc83c-7529-4d86-b778-b3df4267c618}",
            "out_index": 0
        },
        {
            "in_id": "{9b2c7a85-ef3d-44cf-8b99-5a540c4707b4}",
            "in_index": 0,
            "out_id": "{e224c963-f1c5-4825-8562-0ae3eb39b696}",
            "out_index": 0
        },
        {
            "in_id": "{5333dd1c-ecb5-4235-94d0-14ead42b7c77}",
            "in_index": 0,
            "out_id": "{77ff52dd-2b6f-481e-a280-7f2b81da90b9}",
            "out_index": 0
        },
        {
            "in_id": "{7b6af3bd-f6fa-4a52-b764-1a0ddfad2414}",
            "in_index": 0,
            "out_id": "{8dc7f721-0eef-4297-afa9-4a75f06eccad}",
            "out_index": 0
        },
        {
            "in_id": "{bd2aaee5-528a-4c92-a8fe-907e22dd5ff3}",
            "in_index": 0,
            "out_id": "{fe1bc83c-7529-4d86-b778-b3df4267c618}",
            "out_index": 0
        },
        {
            "in_id": "{5333dd1c-ecb5-4235-94d0-14ead42b7c77}",
            "in_index": 1,
            "out_id": "{e672ea0c-a142-44ab-883f-aef3b16086ed}",
            "out_index": 0
        },
        {
            "in_id": "{90dd300d-b6ad-4556-b4dd-701b7ace24e8}",
            "in_index": 1,
            "out_id": "{da2f08e7-a547-4082-973a-38791ed462c0}",
            "out_index": 0
        },
        {
            "in_id": "{1b85d168-4f3a-4108-9d1d-b827b3647a4d}",
            "in_index": 1,
            "out_id": "{90dd300d-b6ad-4556-b4dd-701b7ace24e8}",
            "out_index": 0
        },
        {
            "in_id": "{fe1bc83c-7529-4d86-b778-b3df4267c618}",
            "in_index": 0,
            "out_id": "{26d21317-2ba9-4e38-b176-683f881cf577}",
            "out_index": 0
        },
        {
            "in_id": "{90dd300d-b6ad-4556-b4dd-701b7ace24e8}",
            "in_index": 2,
            "out_id": "{77982881-7d5b-4079-8f78-25b95d764dd7}",
            "out_index": 0
        },
        {
            "in_id": "{1b85d168-4f3a-4108-9d1d-b827b3647a4d}",
            "in_index": 2,
            "out_id": "{2b636439-53b4-4770-9251-056d340a8ebc}",
            "out_index": 0
        },
        {
            "in_id": "{2c1fc74d-27f6-4062-992a-4c21dcf15d24}",
            "in_index": 1,
            "out_id": "{a1ae2f7e-396d-42f8-b98c-9858cea1cbe8}",
            "out_index": 0
        },
        {
            "in_id": "{2b636439-53b4-4770-9251-056d340a8ebc}",
            "in_index": 1,
            "out_id": "{90dd300d-b6ad-4556-b4dd-701b7ace24e8}",
            "out_index": 0
        },
        {
            "in_id": "{698b0166-82c2-451b-bcfe-62471c87e672}",
            "in_index": 1,
            "out_id": "{a1ae2f7e-396d-42f8-b98c-9858cea1cbe8}",
            "out_index": 0
        },
        {
            "in_id": "{0e80d65b-e4e3-4a6d-b1d4-2c9507975f8f}",
            "in_index": 0,
            "out_id": "{2b636439-53b4-4770-9251-056d340a8ebc}",
            "out_index": 0
        },
        {
            "in_id": "{7b6af3bd-f6fa-4a52-b764-1a0ddfad2414}",
            "in_index": 1,
            "out_id": "{a6ad0a30-b14c-444a-8494-1f973bbaa9bc}",
            "out_index": 0
        },
        {
            "in_id": "{a1ae2f7e-396d-42f8-b98c-9858cea1cbe8}",
            "in_index": 2,
            "out_id": "{77982881-7d5b-4079-8f78-25b95d764dd7}",
            "out_index": 0
        },
        {
            "in_id": "{2c1fc74d-27f6-4062-992a-4c21dcf15d24}",
            "in_index": 0,
            "out_id": "{8dc7f721-0eef-4297-afa9-4a75f06eccad}",
            "out_index": 0
        },
        {
            "in_id": "{37b5402a-d0dd-4fae-9c73-76baa381f81d}",
            "in_index": 0,
            "out_id": "{698b0166-82c2-451b-bcfe-62471c87e672}",
            "out_index": 0
        },
        {
            "in_id": "{26d21317-2ba9-4e38-b176-683f881cf577}",
            "in_index": 0,
            "out_id": "{37b5402a-d0dd-4fae-9c73-76baa381f81d}",
            "out_index": 0
        },
        {
            "in_id": "{4b4b0934-8da5-4485-8537-29496c8756d5}",
            "in_index": 0,
            "out_id": "{97680274-6027-46c8-93c4-d553d25b0b4d}",
            "out_index": 0
        },
        {
            "in_id": "{97680274-6027-46c8-93c4-d553d25b0b4d}",
            "in_index": 0,
            "out_id": "{7b6af3bd-f6fa-4a52-b764-1a0ddfad2414}",
            "out_index": 0
        },
        {
            "in_id": "{e672ea0c-a142-44ab-883f-aef3b16086ed}",
            "in_index": 0,
            "out_id": "{97680274-6027-46c8-93c4-d553d25b0b4d}",
            "out_index": 0
        },
        {
            "in_id": "{2c1fc74d-27f6-4062-992a-4c21dcf15d24}",
            "in_index": 2,
            "out_id": "{698b0166-82c2-451b-bcfe-62471c87e672}",
            "out_index": 0
        },
        {
            "in_id": "{5f645217-44e5-472b-ab96-7749696c0743}",
            "in_index": 0,
            "out_id": "{0e80d65b-e4e3-4a6d-b1d4-2c9507975f8f}",
            "out_index": 0
        },
        {
            "in_id": "{e224c963-f1c5-4825-8562-0ae3eb39b696}",
            "in_index": 0,
            "out_id": "{5f645217-44e5-472b-ab96-7749696c0743}",
            "out_index": 1
        },
        {
            "in_id": "{1475f74c-e224-482d-866f-a913e575bb7b}",
            "in_index": 0,
            "out_id": "{26d21317-2ba9-4e38-b176-683f881cf577}",
            "out_index": 1
        },
        {
            "in_id": "{0fdccb05-79e3-4225-a7a3-3be4c1fc0374}",
            "in_index": 0,
            "out_id": "{1475f74c-e224-482d-866f-a913e575bb7b}",
            "out_index": 0
        }
    ],
    "nodes": [
        {
            "id": "{04ee99b3-705f-4f7e-b6b2-c90483acf936}",
            "model": {
                "name": "Comment",
                "text": "Using the node \"Potential Operator\" we can make an operator-representation of our potential . The operator can then be used on different states using \"Apply Operator to State\". "
            },
            "position": {
                "x": 604.7999999999997,
                "y": 1919.8079999999995
            }
        },
        {
            "id": "{7b6af3bd-f6fa-4a52-b764-1a0ddfad2414}",
            "model": {
                "name": "Potential",
                "text": "a*sbox(1.99,2.01,50)"
            },
            "position": {
                "x": 82.78080000000006,
                "y": 1653.5711999999994
            }
        },
        {
            "id": "{8dc7f721-0eef-4297-afa9-4a75f06eccad}",
            "model": {
                "nPoints": "128",
                "name": "Spatial Dimension",
                "xMax": "5",
                "xMin": "-1"
            },
            "position": {
                "x": -708,
                "y": 492
            }
        },
        {
            "id": "{a1ae2f7e-396d-42f8-b98c-9858cea1cbe8}",
            "model": {
                "name": "Potential",
                "text": "b*swell(0,4,10)+b"
            },
            "position": {
                "x": 88.80000000000001,
                "y": 163.19999999999993
            }
        },
        {
            "id": "{e224c963-f1c5-4825-8562-0ae3eb39b696}",
            "model": {
                "n": "0",
                "name": "Get Eigenvalue"
            },
            "position": {
                "x": 2128.3199999999997,
                "y": 647.2800000000001
            }
        },
        {
            "id": "{90dd300d-b6ad-4556-b4dd-701b7ace24e8}",
            "model": {
                "name": "Potential",
                "text": "b*swell(0,4,10)+a*sbox(1.99,2.01,50)+b"
            },
            "position": {
                "x": 29.62559999999999,
                "y": 711.4272000000003
            }
        },
        {
            "id": "{e92ba611-b49a-49c6-90d0-697bc3447561}",
            "model": {
                "name": "Comment",
                "text": "Here the eigenstates and eigenenergies for the complete potential are calculated. "
            },
            "position": {
                "x": 838.0799999999997,
                "y": 552.96
            }
        },
        {
            "id": "{698b0166-82c2-451b-bcfe-62471c87e672}",
            "model": {
                "name": "Hamiltonian"
            },
            "position": {
                "x": 457.19999999999993,
                "y": 186.00000000000003
            }
        },
        {
            "id": "{da2f08e7-a547-4082-973a-38791ed462c0}",
            "model": {
                "name": "Scalar Input",
                "number": "1000"
            },
            "position": {
                "x": -342.3840000000001,
                "y": 714.6719999999999
            }
        },
        {
            "id": "{77982881-7d5b-4079-8f78-25b95d764dd7}",
            "model": {
                "name": "Scalar Input",
                "number": "1000"
            },
            "position": {
                "x": -358.8,
                "y": 797.9999999999997
            }
        },
        {
            "id": "{5333dd1c-ecb5-4235-94d0-14ead42b7c77}",
            "model": {
                "name": "Overlap"
            },
            "position": {
                "x": 1781.0112,
                "y": 1706.1216000000004
            }
        },
        {
            "id": "{2b636439-53b4-4770-9251-056d340a8ebc}",
            "model": {
                "name": "Hamiltonian"
            },
            "position": {
                "x": 622.2719999999999,
                "y": 735.36
            }
        },
        {
            "id": "{1b85d168-4f3a-4108-9d1d-b827b3647a4d}",
            "model": {
                "n": "5",
                "name": "Energy Plot",
                "plotAbs": true,
                "plotEn": true,
                "plotExpect": true,
                "plotImag": true,
                "plotPsin": true,
                "plotReal": true,
                "plotV": true,
                "ymax": "10",
                "ymin": "0"
            },
            "position": {
                "x": 833.0399999999997,
                "y": 982.3200000000002
            }
        },
        {
            "id": "{5f645217-44e5-472b-ab96-7749696c0743}",
            "model": {
                "n": "9",
                "name": "Spectrum"
            },
            "position": {
                "x": 1231.5360000000005,
                "y": 755.3279999999999
            }
        },
        {
            "id": "{c82131ad-e2a1-4952-b01c-4bf2555a4d6e}",
            "model": {
                "name": "Comment",
                "text": "Here we compute the first order correction of the energy for the ground state and 1st excited state respectively. This is done by taking the expectation value of the potential value in the respective states. "
            },
            "position": {
                "x": 1055.8079999999998,
                "y": 1924.9919999999993
            }
        },
        {
            "id": "{2887243d-e75b-4d24-ada7-cd82936a3634}",
            "model": {
                "name": "Comment",
                "text": "Her the perturbation is defined e.g. the delta-function potential. "
            },
            "position": {
                "x": 95.03999999999995,
                "y": 1422.1439999999996
            }
        },
        {
            "id": "{e672ea0c-a142-44ab-883f-aef3b16086ed}",
            "model": {
                "name": "Apply Operator To State"
            },
            "position": {
                "x": 1473.9360000000001,
                "y": 1719.6000000000006
            }
        },
        {
            "id": "{37b5402a-d0dd-4fae-9c73-76baa381f81d}",
            "model": {
                "name": "Hamiltonian Operator"
            },
            "position": {
                "x": 654,
                "y": 193.19999999999993
            }
        },
        {
            "id": "{c41808d2-8c36-4b65-987a-408b60f3aed9}",
            "model": {
                "name": "Comment",
                "text": "Uding the \"Get Eigenvalue\" node we can exstract the energy of the ground state for the unperturbated and the perturbated potential respectively. We observe that the ground state energy of the perturbated potential is greater than the ground state energy of the unperturbated potential. "
            },
            "position": {
                "x": 2638.655999999999,
                "y": 532.2239999999999
            }
        },
        {
            "id": "{26d21317-2ba9-4e38-b176-683f881cf577}",
            "model": {
                "n": "9",
                "name": "Spectrum"
            },
            "position": {
                "x": 925.1999999999998,
                "y": 191.99999999999997
            }
        },
        {
            "id": "{0fdccb05-79e3-4225-a7a3-3be4c1fc0374}",
            "model": {
                "name": "Scalar Output"
            },
            "position": {
                "x": 2405.999999999999,
                "y": 541.1999999999999
            }
        },
        {
            "id": "{11d0fb26-c28e-4617-85e7-383eea78ff44}",
            "model": {
                "name": "Comment",
                "text": "\"Overlap\" takes the inner product between 2 states, and is used to compute the expectation value of the potential energy  in this case. "
            },
            "position": {
                "x": 1083.4559999999994,
                "y": 1473.9840000000004
            }
        },
        {
            "id": "{fe1bc83c-7529-4d86-b778-b3df4267c618}",
            "model": {
                "c1": [
                    1,
                    0
                ],
                "c2": [
                    0,
                    0
                ],
                "c3": [
                    0,
                    0
                ],
                "c4": [
                    0,
                    0
                ],
                "n": "4",
                "name": "Linear Combination",
                "normalizeOutput": true
            },
            "position": {
                "x": 1216.8000000000002,
                "y": 86.40000000000003
            }
        },
        {
            "id": "{77ff52dd-2b6f-481e-a280-7f2b81da90b9}",
            "model": {
                "c1": [
                    0,
                    0
                ],
                "c2": [
                    1,
                    0
                ],
                "c3": [
                    0,
                    0
                ],
                "c4": [
                    0,
                    0
                ],
                "n": "4",
                "name": "Linear Combination",
                "normalizeOutput": true
            },
            "position": {
                "x": 1637.9999999999995,
                "y": 100.79999999999995
            }
        },
        {
            "id": "{f5726103-dada-4be5-8d94-054cd564be18}",
            "model": {
                "name": "Comment",
                "text": "Here the eigenvalues and eigenstates of the unpertubated potential is computed by defining the Hamiltonian and the corresponding operator, whereafter the eigenstates and eigenenergies can be calculated using the node \"Spectrum\". "
            },
            "position": {
                "x": 622.0799999999997,
                "y": -41.47199999999998
            }
        },
        {
            "id": "{4b4b0934-8da5-4485-8537-29496c8756d5}",
            "model": {
                "name": "Apply Operator To State"
            },
            "position": {
                "x": 701.0880000000002,
                "y": 1707.7823999999996
            }
        },
        {
            "id": "{97680274-6027-46c8-93c4-d553d25b0b4d}",
            "model": {
                "name": "Potential Operator"
            },
            "position": {
                "x": 440.352,
                "y": 1698.7007999999998
            }
        },
        {
            "id": "{bd2aaee5-528a-4c92-a8fe-907e22dd5ff3}",
            "model": {
                "name": "Overlap"
            },
            "position": {
                "x": 998.4287999999999,
                "y": 1711.8048000000006
            }
        },
        {
            "id": "{0e80d65b-e4e3-4a6d-b1d4-2c9507975f8f}",
            "model": {
                "name": "Hamiltonian Operator"
            },
            "position": {
                "x": 885.5040000000008,
                "y": 768.6240000000003
            }
        },
        {
            "id": "{2c1fc74d-27f6-4062-992a-4c21dcf15d24}",
            "model": {
                "n": "5",
                "name": "Energy Plot",
                "plotAbs": true,
                "plotEn": true,
                "plotExpect": true,
                "plotImag": true,
                "plotPsin": true,
                "plotReal": true,
                "plotV": true,
                "ymax": "10",
                "ymin": "0"
            },
            "position": {
                "x": 1312.3199999999995,
                "y": 981.1199999999999
            }
        },
        {
            "id": "{0a3f9124-0ba3-4b81-b5d6-a6399c79ad7f}",
            "model": {
                "name": "Comment",
                "text": "Her defineres vores rumlige dimensioner "
            },
            "position": {
                "x": -774,
                "y": 280.8
            }
        },
        {
            "id": "{9b2c7a85-ef3d-44cf-8b99-5a540c4707b4}",
            "model": {
                "name": "Scalar Output"
            },
            "position": {
                "x": 2415.6000000000004,
                "y": 676.7999999999998
            }
        },
        {
            "id": "{1475f74c-e224-482d-866f-a913e575bb7b}",
            "model": {
                "n": "0",
                "name": "Get Eigenvalue"
            },
            "position": {
                "x": 2181.5999999999985,
                "y": 495.6
            }
        },
        {
            "id": "{a6ad0a30-b14c-444a-8494-1f973bbaa9bc}",
            "model": {
                "name": "Scalar Input",
                "number": "1000"
            },
            "position": {
                "x": -203.99999999999997,
                "y": 1638.72
            }
        },
        {
            "id": "{cee3bb0e-358a-4ec6-8a95-383e949d75c0}",
            "model": {
                "name": "Comment",
                "text": "Here the unperturbated potential is defined. To avoid problems with the numerical boundary conditions, the infinite square well is created  using the embedded function swell(a,b,h) which gives a soft well starting in a and ending in b, where h is a parameter which controls the softness of the well. The well must be multiplied with a large scalar in order to approximate an inifinite well. "
            },
            "position": {
                "x": 98.49599999999995,
                "y": -82.94399999999993
            }
        },
        {
            "id": "{67a1f7c6-967c-43d0-acb9-6cfd20927dd2}",
            "model": {
                "name": "Comment",
                "text": "Using the node \"Linear Combination\" we can make the ground state and the 1. excited state of the unperturbated potential. "
            },
            "position": {
                "x": 1468.8000000000002,
                "y": -146.87999999999997
            }
        },
        {
            "id": "{8d16f17e-c785-45fd-b076-930190ac9a11}",
            "model": {
                "name": "Comment",
                "text": "Here the complete potential is defined. The delta bump is made by placing a narrow soft box in the middle of the infinite well using the embedded function sbox(a,b,h),  which makes a box starting in a and b, where h is a parameter which controls the softness of the well. "
            },
            "position": {
                "x": 5.183999999999955,
                "y": 489.0239999999999
            }
        },
        {
            "id": "{7385fa53-3a89-4ab4-94fe-dd8d1358505f}",
            "model": {
                "name": "Comment",
                "text": "Here is an \"Energy Plot\" for the unperturbated and the complete potential respectively. On should notice that the even solutions approaches the odd solutions under this perturbation. "
            },
            "position": {
                "x": 1762.559999999999,
                "y": 1092.095999999999
            }
        },
        {
            "id": "{c20a3cf6-d546-45d3-ba57-38c89b672b19}",
            "model": {
                "name": "Comment",
                "text": "The first order correction is very large for even states whilst the energy of the odd states remains the same - the small correction is due to us approximating the delta-function with a box. "
            },
            "position": {
                "x": 1622.5919999999994,
                "y": 1914.6239999999998
            }
        }
    ]
}