Question

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?

Answer #1

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?

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.

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?

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,...

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...

Suppose initially a particle is in the ground state of a
1-dimensional inﬁnite square well which extends from x = 0 → a. The
wall of the square well is suddenly moved to 2a, so the square well
now extends from x = 0 → 2a. What is the probability of ﬁnding the
particle in the n = 3 state of the new (larger) square well?

Consider the time-dependent ground state wave function
Ψ(x,t ) for a quantum particle confined to an
impenetrable box.
(a) Show that the real and imaginary parts of Ψ(x,t) ,
separately, can be written as the sum of two travelling waves.
(b) Show that the decompositions in part (a) are consistent with
your understanding of the classical behavior of a particle in an
impenetrable box.

The purpose of this problem is to compare the time dependencies
for systems in a superposition of two energy eigenstates in an
infinite square well to those in a simple harmonic
oscillator.
Consider two systems (an infinite square well and a simple harmonic
oscillator) that have the same value for their ground state energy
Eground.
1) What is E3, the energy of the 2nd excited
state (the third lowest energy) of the infinite square well system
in terms of Eground?...

The purpose of this problem is to compare the time dependencies
for systems in a superposition of two energy eigenstates in an
infinite square well to those in a simple harmonic
oscillator.
Consider two systems (an infinite square well and a simple harmonic
oscillator) that have the same value for their ground state energy
Eground.
1) What is E3, the energy of the 2nd excited
state (the third lowest energy) of the infinite square well system
in terms of Eground?...

The purpose of this problem is to compare the time dependencies
for systems in a superposition of two energy eigenstates in an
infinite square well to those in a simple harmonic
oscillator.
Consider two systems (an infinite square well and a simple harmonic
oscillator) that have the same value for their ground state energy
Eground.
1) What is E3, the energy of the 2nd excited
state (the third lowest energy) of the infinite square well system
in terms of Eground?...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 25 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 48 minutes ago

asked 50 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago