Wavefunction \(\psi(x)\)
Probability Density \(|\psi(x)|^2\) Stationary eigenstate: probability density does not change in time.
Potential and Energy Levels

Quantum State Controls

0
1

Display Controls

2.0

Relevant Equations

Wavefunction:
\(\psi_n(x) = \left(\frac{m\omega}{\pi\hbar}\right)^{1/4} \frac{1}{\sqrt{2^n n!}} e^{-\frac{m\omega x^2}{2\hbar}}\, H_n\!\left(\sqrt{\frac{m\omega}{\hbar}}\,x\right)\)
\(H_n(x)\) are the Hermite polynomials.
Energy levels:
\(E_n = \hbar\omega\left(n + \tfrac{1}{2}\right)\)

Current Quantum State

Current wavefunction:
\(\psi(x,t) = \psi_{0}(x)\,e^{-iE_{0}t/\hbar}\)
Current energy eigenvalue:
\(E_0 = 0.5\,\hbar\omega\)

Statistics

FPS
60
Phase
0.00
Parity
Even