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SOLVED:Write the normalized form of the ground state wavefunction of the harmonic oscillator in terms of the variable y and the parameter α. (a) Write the integral you would need to evaluate to find the mean displacement ⟨y⟩, and then use a symmetry argument to explain why this integral is equal to 0. (b) Calculate ⟨y^2⟩(the necessary integral will be found in the Resource section ). (c) Repeat the process for the first excited state.
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SOLVED:The ground-state wavefunction of a hydrogen atom has the form ψ(r)=N e^-b r, b being a collection of fundamental constants with the magnitude 1 / a0, with a0=53 pm Normalize this spherically symmetrical function. Hint. The volume element is d τ=sinθd θd φr^2 d r, with 0 ≤θ≤π0 ≤φ≤2 π, and 0 ≤r<∞, 'Normalize' always means 'normalize to 1 ' in this text.
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