- #1

Robsta

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## Homework Statement

The wavefunction ψ(x,t) obeys the time-dependent Schrodinger equation for a free particle of mass m moving in one dimension.

Show that a second wavefunction φ(x,t) = e

^{i(ax-bt)}ψ(x-vt , t) obeys the same time dependent schrodinger equation, provided a = ħa

^{2}/2m and v = ħa/m

## Homework Equations

The time dependent schrodinger equation is iħ∂φ/∂t = Hφ

Hφ = -ħ

^{2}/2m * ∂

^{2}φ/∂x

^{2}

## The Attempt at a Solution

Taking the partial derivative of φ with respect to t, and using the product rule, you have to take ∂ψ(x-vt, t)/∂t and I'm not sure how to do this.