The wave function ψ ( x ) = A e i k x is a solution to the one dimensional Schrodinger equation − ℏ 2 2 m d 2 ψ ( x ) d x 2 + U ( x ) ψ ( x ) = E ψ ( x ) . Determine the expression for k and relate it with particles momentum and de Broglie wavelength.

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Chapter 40, Problem 50E

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To show: The wave function ψ(x)=Aeikx is a solution to the one dimensional Schrodinger equation −ℏ22md2ψ(x)dx2+U(x)ψ(x)=Eψ(x) . Determine the expression for k and relate it with particles momentum and de Broglie wavelength.

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