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By employing the prescribed definitions of the raising and lowering operators pertaining to the one-dimensional harmonic oscillator: x = ħ - (â+ + â_) 2mw hmw p = i - (â+ − â_) 2 Compute the expectation values of the following quantities for the nth stationary staten. Keep in mind that the stationary states form an orthogonal set. [ 4m4ndx = 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 n

By employing the prescribed definitions of the raising and lowering operators pertaining to the one-dimensional harmonic oscillator: x = ħ - (â+ + â_) 2mw hmw p = i - (â+ − â_) 2 Compute the expectation values of the following quantities for the nth stationary staten. Keep in mind that the stationary states form an orthogonal set. [ 4m4ndx = 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 n

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By 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 n
Transcribed Image Text:By 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 n
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how do you determine what the values of the rising and lowering operators are? (how did you get these values of a+ and a-)

we know that ât is r is rising operator and a_ is a lowering operator. â+In> = √n+in+1) â-|m>= √n Inds
Transcribed Image Text:we know that ât is r is rising operator and a_ is a lowering operator. â+In> = √n+in+1) â-|m>= √n Inds
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