Question

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

Answer #1

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

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>. .

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.

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

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

A harmonic oscillator with mass m and force constant k is in an
excited state that has quantum number n.
1)
Let pmax=mvmaxx, where vmax is the maximum speed calculated in
the Newtonian analysis of the oscillator. Derive an expression for
pmax in terms of n, ℏ, k, and m.
Express your answer in terms of the variables n, k, m, and the
constant ℏ
2)
Derive an expression for the classical amplitude A in terms of
n, ℏ, k,...

For a particle in the harmonic oscillator potential, calculate
the followings in any stationary state n:
a) 〈?̂?̂〉? b) 〈?̂?̂〉? c) 〈[?̂, ?̂]〉n

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