Quantum Mechanics Operators question

[zheng89120]

Homework Statement

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

Homework Equations

Commutator calculation and properties

? Time-independent Schrödinger equation and solution

The Attempt at a Solution

QH-HQ = E_oQ

Q = (QH-HQ)/E_o

Qψ = QC₁e^iA1/2x+QC₂e^-iA1/2x

 

[nicksauce]

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