Question

The infinite potential well has zero potential energy between 0 and a, and is infinite elsewhere.

a) What are the energy eigenstates of this quantum system, and what are their energies? In the case of a discrete spectrum, explain where the quantization comes from.

b) Suppose we take the wavefunction at a given time to be an arbitrary function of x that is symmetric around the center of the well (at x = a/2). Is this a stationary state in general? Briefly explain your answer.

c) Start with the wavefunction of b), measure the location, and then wait for an hour and measure the energy of the state. Which outcomes are possible?

d) Suppose we start with the particle in its groundstate. At some point the well doubles in size, and extends from 0 to 2a (while the wavefunction is still given by the groundstate of the smaller well). What are the possible outcomes of an energy measurement of this system?

Answer #1

A particle is in the ground state of an infinite square well.
The potential wall at x = L suddenly (i.e., instantaneously) moves
to x = 3L. such that the well is now three times its original size.
(a) Let t = 0 be at the instant of the sudden change in the
potential well. What is ψ(x, 0)?
(b) If you measure the energy of the particle in the new well,
what are the possible energies?
(c) Estimate the...

Given three non-interacting distinguishable in an infinite 1-D
square well potential of width a.
(a) Determine the ground wave function for the system of
distinguishing and the energy of this state.
(b) Determine the wave function of the first excited state and
its energy.

Consider a particle trapped in an infinite square well potential
of length L. The energy states of such a particle are given by the
formula: En=n^2ℏ^2π^2 /(2mL^2 ) where m is the mass of the
particle.
(a)By considering the change in energy of the particle as the
length of the well changes calculate the force required to contain
the particle. [Hint: dE=Fdx]
(b)Consider the case of a hydrogen atom. This can be modeled as
an electron trapped in an infinite...

II(20pts). Short Problems
a) The lowest energy of a particle in an infinite one-dimensional
potential well is 4.0 eV. If the width of the well is doubled, what
is its lowest energy?
b) Find the distance of closest approach of a 16.0-Mev alpha
particle incident on a gold foil.
c) The transition from the first excited state to the ground
state in potassium results in the emission of a photon with = 310
nm. If the potassium vapor is...

1. As we increase the quantum number of an electron in a
one-dimensional, infinite potential well, what happens to the
number of maximum points in the probability density function?
It increases.
It decreases.
It remains the same
2. If an electron is to escape from a one-dimensional, finite
well by absorbing a photon, which is true?
The photon’s energy must equal the difference between the
electron’s initial energy level and the bottom of the nonquantized
region.
The photon’s energy must...

In this problem we are interested in the time-evolution of the
states in the infinite square potential well. The time-independent
stationary state wave functions are denoted as ψn(x) (n = 1, 2, . .
.).
(a) We know that the probability distribution for the particle
in a stationary state is time-independent. Let us now prepare, at
time t = 0, our system in a non-stationary state
Ψ(x, 0) = (1/√( 2)) (ψ1(x) + ψ2(x)).
Study the time-evolution of the probability...

Learning Outcomes (Unit 2)
Perform quantitative calculations based on the relationship
between wavelength, energy, and the speed of light.
Identify and rank the different types of radiation which
comprise the electromagnetic spectrum.
Explain why classical mechanics doesn't describe electromagnetic
radiation.
Describe the photoelectric effect and relate the energy and/or
intensity of the photons to the work function and kinetic energy of
the ejected electrons.
Explain the origin of atomic and emission spectra and relate
these spectra to discrete energy levels....

QUESTION 1
? What is the relationship between family dysfunction and
schizophrenia?
a.
?Research has substantiated a link between family dysfunction
and schizophrenia but can't say which causes the other.
b.
?Family dysfunction is a major causative factor for
schizophrenia.
c.
?Research has failed to substantiate a direct causal link
between family dysfunction and schizophrenia.
d.
?Family dysfunction plays a minor role in developing
schizophrenia.
1.00000 points
QUESTION 2
? Chuck has no life plan; he simply lives from...

Please read the article and answear about
questions.
Determining the Value of the Business
After you have completed a thorough and exacting investigation,
you need to analyze all the infor- mation you have gathered. This
is the time to consult with your business, financial, and legal
advis- ers to arrive at an estimate of the value of the business.
Outside advisers are impartial and are more likely to see the bad
things about the business than are you. You should...

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