State Analysis

In this section the nodes for the state analysis is presented. In order to do so a simple system with the infinite well as a potential is used along with the ground state $ \psi_g(x) = \psi_1(x) $ and the superposition $\psi_s(x) = \psi_1(x) + \psi_2(x)$. 

We investigate the

  • The expectation value $\langle \hat{O} \rangle$
  • The squared expectation value $\langle \hat{O}^2 \rangle$
  • The standard deviation $\sigma$
  • The variance $\sigma^2$

with the position operator on the superposition state $\psi_s$. 

The overlap between the two states $\psi_g$ and $\psi_s$  can be found using the node $\langle \psi | \psi \rangle $. 
The fidelity between the two states can be found using the fidelity node $| \langle \psi | \phi \rangle |^2$. 
If you would like to investigate a portion of the distribution in an interval use the integration node. $\int |\psi|^2$