Effect of Hamiltonian on Trial Wavefunction

What is the result of operating on the function

with the Hamiltonian Operator

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(see Dykstra's 'Physical Chemistry, A Modern Introduction', page 252). Write your answer as a product of a polynomial in x and and exponential, i.e., in as compact a form as possible. Use `beta' for , `hbar', `m', and `exp()' as needed. Include all multiplication signs, and be careful about brackets. Use `^' or `**' for powers, i.e., x^2 = x**2 = x squared.
Answer =
Query, is the above answer correct?

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