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Question: if a trial wavefunction x satisfies the schrdinger equation...

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If a trial wavefunction ψ(x) = e^{-eta x^{2}} satisfies the Schrödinger equation for a harmonic oscillator with a force constant of k and a reduced mass of μ,

(a) What is the expression of β in terms of k and μ?

(b) What is the total energy E corresponding to the state described by this wavefunction?

(c) Is this wavefunction the eigenfunction of the kinetic energy operator (Kˆ)? Is it the eigenfunction of the potential energy operator (Vˆ)? If yes, find the eigen values for these two operators.

(7) If a trial wavefunction ψ(x)-e-Ar satisfies the Schrödinger equation for a harmonic oscillator with a force constant of k

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