Hamiltonian

Hamiltonians represent the energy in a system and generate dynamics. This Hamiltonian describes the situation of a single particle in a potential.

Input

  • x: Spatial Dimension
  • V: Potential

 Output

  • H: Hamiltonian

Content

The textfield shows what is being calculated inside the node: the sum of the kinetic and potential energy-operators T and V. The kinetic operator $T = \frac{-\hbar^2}{2m} \frac{\partial^2}{\partial x^2}$ is calculated from the spatial dimension x, while the potential is taken from the input. Note, that because of the natural Units we use, the kinetic term becomes somewhat simplified.