By employing the prescribed definitions of the raising and lowering operators pertaining to the one-dimensional harmonic oscillator: x = ħ 2mw ·(â+ + â_) ħmw 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 2mw ·(â+ + â_) ħmw 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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just parts d and e please :) thanks
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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