Question

Quantum mechanics:

Consider a particle initially in the ground state of the
one-dimensional simple harmonic oscillator. A uniform electric
field is abruptly turned on for a time t and then abruptly turned
off again. What is the probability of transition to the first
excited state?

Answer #1

Quantum mechanics problem: Consider a particle
initially in the ground state of the one-dimensional simple
harmonic oscillator. A uniform electric field is abruptly turned on
for a time t and then abruptly turned off again. What is the
probability of transition to the first excited state?

Consider a one-dimensional harmonic oscillator, in an energy
eigenstate initially (at t=t0), to which we apply a time
dependent force F(t).
Write the Heisenberg equations of motion for x and for p.
Now suppose F is a constant from time t0 to time
t0+τ(tau), and zero the rest of the time. Find the
average position of the oscillator <x(t)> as a function of
time, after the force is switched off.
Find the average amount of work done by the force,...

A quantum-mechanical system initially in its ground level
absorbs a photon and ends up in the first excited state. The system
then absorbs a second photon and ends up in the second excited
state. For which of the following systems does the second photon
have a longer wavelength than the first one?
(a) a harmonic oscillator;
(b) a hydrogen atom;
(c) a particle in a box.
Briefly motivate your answer.

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

quantum physics:
Considera particle in the ground state of an infinite square well
where the left half of the well rises at a linear rate to a
potential of V0in a time t, and then falls back at a linear rate in
a time t. What is the probability that the particle is now in the
first excited state?

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...

The sides of a one dimensional quantum box (1-D) are
in x=0, x=L. The probability of observing a particle of mass m in
the ground state, in the first excited state and in the 2nd excited
state are 0.6, 0.3, and 0.1 respectively
a) If each term contributing to the particle function
has a phase factor equal 1 in t=0. What is the wave function for
t>0?
b) what is the probability of finding the particle at
the position x=L/3...

Consider an electron bound in a three dimensional simple
harmonic oscillator potential in the n=1 state. Recall that the
e- has spin 1/2 and that the n=1 level of the oscillator
has l =1. Thus, there are six states {|n=1, l=1, ml,
ms} with ml= +1, 0, -1 and ms =
+/- 1/2.
- Using these states as a basis find the six states with
definite j and mj where J = L +s
- What are the energy levels...

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