A particle of mass m moves in a region in which the potential energy is constant, V

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A particle of mass m moves in a region in which the potential energy is constant, V = V0.

(a) Show that neither Ψ(x,t) = Asin(kx - ωt) nor Ψ(x,t) = Acos (kx-ωt) satisfies the time-dependent Schrödinger equation.

(b) Show that Ψ(x, t) = A[cos(kx - ωt) + isin (kx - ωt)] = Aei(kx - ωt) does satisfy the time-independent Schrödinger equation provided that k, V0, and v are related by Equation 6-5.

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Modern Physics

ISBN: 9781429250788

6th Edition

Authors: Paul A. Tipler, Ralph Llewellyn

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