Spectrum

Description

This node calculates the eigenstates and eigenvalues of the system defined by the Hamiltonian.

Input

The node has the following input: 

  • Hamiltonian ($H$): It inputs the Hamiltonian node.

Content

In the content field, $N_{eigenstates}$ corresponds to the number of eigenstates and eigenvalues that will be calculated and sent to the output. For "1", the node calculates the first eigenstate & eigenvalue of the system, which is the ground state.

By default, it is set at ''2'' and it can be changed to a higher number to output more than two eigenstates & eigenvalues.

Output

  • Spectrum of eigenstates ($\{ \psi_n \}$): The list of eigenstates of the system defined by the Hamiltonian.
  • Spectrum of eigenvalues ($\{ E_n \} $): The list of eigenvalues of the corresponding eigestates of the system.

Example

In the example below, the spectrum of a harmonic oscillator is calculated. The content field reads ''5'' which means that it will ouput the first 5 eigenstates and eigenvalues of this system.