Question

Calculate the expectation value of momentum for the second excited state of the harmonic oscillator. Show steps for both integral and bracket notation please.

Answer #1

Calculate the standard deviation of momentum for the second
excited state of a harmonic oscillator.

For a particle in the first excited state of harmonic oscillator
potential,
a) Calculate 〈?〉1, 〈?〉1, 〈? 2〉1, 〈? 2〉1.
b) Calculate (∆?)1 and (∆?)1.
c) Check the uncertainty principle for this state.
d) Estimate the length of the interval about x=0 which
corresponds to the classically allowed domain for the first excited
state of harmonic oscillator.
e) Using the result of part (d), show that position uncertainty
you get in part (b) is comparable to the classical range of...

Q. 2(a) For the first excited state of harmonic oscillator,
calculate <x>, <p>, <x2>, and <p2>
explicitly by spatial integration. (b) Check that the
uncertainty principle is obeyed.
(c) Compute <T> and <V>. .

Compute the expectation value and standard deviation of position
for the ground state of the harmonic oscillator.

Consider the ground state of the harmonic oscillator.
(a) (7 pts) Calculate the expectation values <x>,
<x2>, <p> and <p2>.
(b) (3 ps) What is the product ΔxΔp, where the two quantities
are standard deviations? (This is easy if you did part (a)). How
does this answer compare with the prediction of the Uncertainty
Principle?

A quantum mechanical simple harmonic oscillator has a 1st
excited state with energy 3.3 eV and there are eight spin 1⁄2
particles in the oscillator. How much energy is needed to add a
ninth electron. Explain and show your work.

A quantum mechanical simple harmonic oscillator has a 1st
excited state with energy 3.3 eV and there are eight spin-1/2
particles in the oscillator. How much energy is needed to add a
ninth electron. Explain and show your work

A quantum mechanical simple harmonic oscillator has a 1st
excited state with energy 3.3 eV and there are eight spin-1/2
particles in the oscillator. How much energy is needed to add a
ninth electron. Explain and show your work

a)
For a 1D linear harmonic oscillator find the first order
corrections to the ground state due to the Gaussian perturbation.
b) Find the first order corrections to the first excited
state.
Please show all work.

For the simple harmonic oscillator at first excited state the
Hermite polynomial H1=x, (a)find the
normalization constant C1 (b) <x> (c)
<x2>, (d) <V(x)> for this
state.

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