Let ₁ (x) and ₂ (x) be normalized stationary states (energy eigenfunctions) of an one-dimensional system for unequal energies E₁ and E2. Let Y (x; t) be the wave function ofthe system, and suppose that at t = 0 it is given byY (x; t = 0) = A[ ¥₁ (x) + (1 - i) 4₂ (x)]a) Determine A such that Y (x; t = 0) is normalized.b) Write down the wave function Y (x; t) at time t. Is Y (x; t) a stationary state? Explain.c) Does the probability density |Y (x; t)|² vary with time?

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Let ¥₁ (x) and ↳₂2 (x) be normalized stationary states (energy eigenfunctions) of an one- dimensional system for unequal energies E₁ and E2. Let Y (x; t) be the wave function of the system, and suppose that at t = 0 it is given by Y (x; t = 0) = A[ ¥₁ (x) + (1 - i) Y₂ (x)] a) Determine A such that Y (x; t = 0) is normalized. b) Write down the wave function Y (x; t) at time t. Is Y (x; t) a stationary state? Explain. c) Does the probability density |Y (x; t)|² vary with time?

Let ¥₁ (x) and ↳₂2 (x) be normalized stationary states (energy eigenfunctions) of an one- dimensional system for unequal energies E₁ and E2. Let Y (x; t) be the wave function of the system, and suppose that at t = 0 it is given by Y (x; t = 0) = A[ ¥₁ (x) + (1 - i) Y₂ (x)] a) Determine A such that Y (x; t = 0) is normalized. b) Write down the wave function Y (x; t) at time t. Is Y (x; t) a stationary state? Explain. c) Does the probability density |Y (x; t)|² vary with time?

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