In the harmonic oscillator problem, the normalized wave functions for the ground and first excited states...

In the harmonic oscillator problem, the normalized wave functions for the ground and first excited states are ψ₀ and ψ₁. Using these functions, at some point t, a wave function u = Aψ₀ + Bψ₁ is constructed, where A and B are real numbers.
(a) Show that the average value of x in the u state is generally non-zero.

(b) What condition A and B must satisfy if we want the function u to be normalized?

(c) For which values of the constants A and B do we get the maximum and for which minimum of <x>?

The result:

(b) A² + B² = 1
(c) Maximum: A = B = 2^−1/2

Expert Solution

genius_generous answered 2 years ago

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