6. Show that $Ae^{i(kx-wt)}$ satisfies the time-dependent Schrödinger wave equation.
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Step 1: Start with the time-dependent Schrödinger wave equation: \[i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \Psi}{\partial x^2}\] Show more…
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Madhur L.
5. (a) Show that for a free particle of mass m moving in one dimension, the function ψ(x) = A sin(kx) + B cos(kx) is a solution to the time-independent Schrödinger equation for any values of the constants A and B. (b) Show that the wave function ψ(x,t) = Ae^{kx - ωt} does not satisfy the time-dependent Schrödinger equation.
(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.
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