# Quantum Harmonic Oscillator

mark18

## Homework Statement

H = p^2/2m + (kx^2)/2 - qAx (THis is a harmonic potentional with external electric force in 1D)

Braket:
Definitions:
|0, A=0 > = |0>_0 for t=0 (ground state)
|0, A not 0 > = |0> for t=0 (ground state)

2. Question
1. Find the probability of being in the state |0, A not 0> for t>=0 when you are in the state |0>_0
2. Find the coefficients for the station |0>_0 = Sigma_k c_k |k>

## The Attempt at a Solution

1.
P = |<0, A not 0|e^(-iE_0t)|0, A=0 >|^2 = <0, A not 0||0, A=0 >^2 = ? (how to find this, do i go over to position representation?)
i've tried that but got an answer which didn't depend of t??? since t factor is being cancelled out by the complex conjugation.

2. c_k = < k | | 0 >_0 = ?

Last edited: