Question

Consider an electron in a one-dimensional potential well of
width L_{z} in the z direction, with infinitely high
potential barriers on either side (i.e., at z = 0 and z =
L_{z} ). For simplicity, we assume the potential energy is
zero inside the well. Suppose that at time t = 0 the electron is in
an equal linear superposition of its lowest two energy eigenstates,
with equal real amplitudes for those two components of the
superposition.

(i) Write down the wavefunction at time t = 0 such that it is normalized. (ii) Starting with the normalized wavefunction at time t = 0 , write down an expression for the wavefunction valid for all times t. (iii) Show explicitly whether this wavefunction is normalized for all such times t.

Answer #1

4.
An electron is trapped in a one-dimensional infinite potential well
of width L.
(1) Find wavefunction ψn(x) under assumption that the
wavefunction in 1 dimensional box whose potential energy U is 0 (0≤
z ≤L) is normalized
(2) Find eighenvalue En of electron
(3) If the yellow light (580 nm) can excite the elctron from
n=1 to n=2 state, what is the width (L) of petential well?

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...

An electron is trapped in an infinite one-dimensional well of
width = L. The ground state energy for this electron is 3.8
eV.
a) Calculated energy of the 1st excited state.
b) What is the wavelength of the photon emitted between 1st
excited state and ground states?
c) If the width of the well is doubled to 2L and mass is halved
to m/2, what is the new 3nd state energy?
d) What is the photon energy emitted from the...

An electron is in an infinite one-dimensional square well of
width L = 0.12 nm.
1) First, assume that the electron is in the lowest energy
eigenstate of the well (the ground state). What is the energy of
the electron in eV? E =
2) What is the wavelength that is associated with this
eigenstate in nm? λ =
3) What is the probability that the electron is located within
the region between x = 0.048 nm and x =...

choose all of the following statements that are correct for a
particle in a one dimensional infinite square
a,)the stationary states refers to eigenstates of any operator
corresponding to physical observable
b)in an isolated system if a particle has well -defined position
at time = 0 the position of the particle is well defined at all
times t>0
c)in an isolated system if an energy eigenstate at time t=0 the
energy of the particle is well defined at all times...

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...

1 - Write the one dimensional, time-independent Schrödinger
Wave Equation (SWE). Using the appropriate potential energy
functions for the following systems, write the complete time
independent SWE for:
(a) a particle confined to a one-dimensional infinite square
well,
(b) a one-dimensional harmonic oscillator,
(c) a particle incident on a step potential, and
(d) a particle incident on a barrier potential of finite width.
2 - Find the normalized wavefunctions and energies for the
systems in 1(a). Use these wavefunctions to...

Suppose that an electron trapped in a one-dimensional infinite
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the state with n = 5.
1 What energy must be transferred to the electron for this
quantum jump?
2 The electron then de-excites back to its ground state by
emitting light. In the various possible ways it can do this, what
is the shortest wavelengths that can be emitted?
3 What is the second shortest?
4 What...

4. Consider a free electron bound within a 2-dimensional
infinite potential well defined by V = 0 for 0 < x < 25 Å, 0
< y < 50 Å, and V = ∞ elsewhere. Determine the expression for
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An infinitely deep square well has width L = 2.5 nm.
The potential energy is V = 0 eV inside the well
(i.e., for 0 ≤ x ≤ L). Seven electrons
are trapped in the well.
1) What is the ground state (lowest) energy of this seven
electron system in eV?
Eground =
2) What is the energy of the first excited state of the system
in eV?
NOTE: The first excited state is the one that has the lowest...

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