Question

(a) Show that the wave function ?(x,t) = Acos(kx? ?t) does not satisfy the time-dependent Schrödinger equation with V = 0, or ? ?²/2m ?²?/?x² = i? ??/?t . (b) Show that the wave function ?(x,t) = Aexp(ikx?i?t) does satisfy the time-dependent Schrödinger equation.

          (a) Show that the wave function ?(x,t) = Acos(kx? ?t) does not satisfy the time-dependent Schrödinger
equation with V = 0, or ? ?²/2m ?²?/?x² = i? ??/?t .

(b) Show that the wave function ?(x,t) = Aexp(ikx?i?t) does satisfy the time-dependent Schrödinger
equation.

(a) Show that the wave function ?(x,t) = Acos(kx? ?t) does not satisfy the time-dependent Schrödinger
equation with V = 0, or ? ?²/2m ?²?/?x² = i? ??/?t .

(b) Show that the wave function ?(x,t) = Aexp(ikx?i?t) does satisfy the time-dependent Schrödinger
equation.

Added by Francisco J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Mehdi Hatefipour

06/15/2021

Step 1

First, let's recall the time-dependent Schrödinger equation: iħ ∂ψ/∂t = -ħ²/2m ∂²ψ/∂x² + Vψ where i is the imaginary unit, ħ is the reduced Planck constant, m is the mass of the particle, V is the potential energy, and ψ is the wave function. Show more…

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(a) Show that the wave function Ψ(x,t) = Acos(kx− ωt) does not satisfy the time-dependent Schrödinger equation with V = 0, or −ℏ²/2m ∂²Ψ/∂x² = iℏ ∂Ψ/∂t. (b) Show that the wave function Ψ(x,t) = Aexp(ikx−iωt) does satisfy the time-dependent Schrödinger equation.