show that the following wave function is normalized.
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show that the following wave function is normalized. Remember to square it first. Show full and complete procedure do not skip any part of the steps
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4√/2π
(2 — r)e-¹/²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc614cc7d-1c60-4824-bcc7-4e759b37d40e%2F99266de9-f3c0-4e90-805c-cc4955627a35%2Fvpduth8j_processed.png&w=3840&q=75)
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The complex conjugate of above equation is
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- a particle is confined to move on a circle's circumference (particle on a ring) such that its position can be described by the angle ϕ in the range of 0 to 2π. This system has wavefunctions in the form Ψm(ϕ)= eimlϕ where ml is an integer. Show that the wavefunctions Ψm(ϕ) with ml= +1 and +2 are ORTHOGONAL Show full and complete procedure. Do not skip any stepBy employing the prescribed definitions of the raising and lowering operators pertaining to the one-dimensional harmonic oscillator: x = ħ 2mω -(â+ + â_) hmw ê = i Compute the expectation values of the following quantities for the nth stationary staten. Keep in mind that the stationary states form an orthogonal set. 2 · (â+ − â_) [ pm 4ndx YmVndx = 8mn a. The position of particle (x) b. The momentum of the particle (p). c. (x²) d. (p²) e. Confirm that the uncertainty principle is satisfied for all values of nNeed full detailed answer.