The Hamiltonian operator for a one-dimensional harmonic oscillator moving in the x direction is Find the value

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The Hamiltonian operator for a one-dimensional harmonic oscillator moving in the x direction is

h? d? kx? Н- 2m dx2 2

Find the value of the constant a such that the function eˆ’ax2 is an eigenfunction of the Hamiltonian operator and find the eigenvalue E. The quantity k is the force constant, m is the mass of the oscillating panicle, and „ is Planck€™s constant divided by 2Ï€.

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