(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\psi(x,0) = N exp[-\alpha(x-a)^2][/tex]

(1):This wavefunction is a solution to the time dependent schrödinger equation for a harmonic oscillator, but not to the time independent one. How is that possible?

(2):Explain without calculating how would you find the time dependent wave function [tex]\psi(x,t)[/tex]?

2. Relevant equations

3. The attempt at a solution

(1)According to my book it seems to explain that any solution to the schrödinger equation can be explained by a linear combination of the basis states.

I would assume that if [tex]\psi(x,t)[/tex] is a linear combination of time dependent basis states, that [tex]\psi(x,0)[/tex] would also be a linear combination of time independent basis states, and that [tex]\psi(x,t)[/tex] consist of the same basis states as [tex]\psi(x,0)[/tex] except that each basis state is multiplied with the time dependent factor [tex]exp[-iEn*t/h][/tex]. In that case, [tex]\psi(x,0)[/tex] would be a solution, but it is not. So im stuck in this contradiction.

(2)To find the time dependent state, i would try to identify the basis time independent states describing the wave function. Then multiply each basis state with the corresponding [tex]exp[-iEn*t/h][/tex] factor. However i cant identify any basis time independent states if any in [tex]\psi(x,0)[/tex].

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Harmonic oscillator special state (QM)

**Physics Forums | Science Articles, Homework Help, Discussion**