The wave function of a quantum particle of mass m is ψ(x) = A cos (kx) + B sin (kx)where A, B, and k are constants. (a) Assuming the particle is free (U = 0), show that ψ(x) is a solution of the Schrödinger equation (as shown). (b) Find the corresponding energy E of the particle. The Schrödinger equation as it applies to a particle of mass m confined tomoving along the x axis and interacting with its environment through a potentialenergy function U(x) ish? d?+ Uựp = Ep(40.15)2m dx?

Answered: Image /qna-images/answer/0645e281-7770-414e-89f5-d2b4df472725.jpg

The Schrödinger equation as it applies to a particle of mass m confined to moving along the x axis and interacting with its environment through a potential energy function U(x) is h? d? + Uựp = Ep (40.15) 2m dx?

The Schrödinger equation as it applies to a particle of mass m confined to moving along the x axis and interacting with its environment through a potential energy function U(x) is h? d? + Uựp = Ep (40.15) 2m dx?

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Question

The wave function of a quantum particle of mass m is
ψ(x) = A cos (kx) + B sin (kx)
where A, B, and k are constants. (a) Assuming the particle is free (U = 0), show that ψ(x) is a solution of the Schrödinger equation (as shown). (b) Find the corresponding energy E of the particle.