# Quantum Mechanics Operators question

1. Jul 7, 2010

### zheng89120

1. The problem statement, all variables and given/known data

The operator Q obeys the commutation relation [Q, H] = EoQ, where Eo is a constant with units of energy. Show that if ψ(x) is a solution of the time-independent Schrodinger equation with energy E, then Qψ(x) is also a solution of the time-independent Schrodinger equation, and determine the energy corresponding to Qψ(x).

2. Relevant equations

Commutator calculation and properties

? Time-independent Schrodinger equation and solution

3. The attempt at a solution

QH-HQ = EoQ

Q = (QH-HQ)/Eo

Qψ = QC1eiA1/2x+QC2e-iA1/2x

2. Jul 7, 2010

### nicksauce

Your approach seems a little strange. ψ satisfies Hψ = Eψ (the time independent Schrodinger equation). Then write an expression for H(Qψ) by using the commutator you are given and the fact that Hψ = Eψ.