Physics 115A Midterm #2 Solutions
Sean Litsey
May 29, 2014
Problem 1
Part a
We are given the wavefunction
(x) = A (2 (x) + 3 (x)
(1)
where
nx
2
sin
a
a
n (x) =
(2)
are the eigenfunctions of the innite square well Hamiltonian, with eigenvalues (i.e. energ
Physics 115B Problem Set #1 Solutions
Sean Litsey
April 15, 2014
Problem 1
We would like to show that the energy density u and emissive power E for a cavity are related by
4
E (, T ) .
c
u (, T ) =
(1)
To do this, we need to understand how these two quant
Problem Set 1 (due 4/7)
(Physics 115A, Fall 2014, H. W. Jiang)
1. Show that the relation between the energy density in a cavity, u(, T) and the emissive
power, E(,T) is given by,
u(,T)=4E(,T)/c
[Hint: To do so, look at the figure. The shaded volume elemen
HW #9 (due Friday, 12/2)
(Physics 115A, Fall 2016)
1. Derive the following inverse Fourier transform relation using the Dirac bra-ket
notation.
( p)
1
2
dx( x)e
ipx /
2. Consider a particle in a one-dimensional infinite potential box of length a. Its w
Quantum Mechanics HW 4 (Solutions)
Matthew Poulos
UCLA Department of Physics
(Dated: October 26, 2016)
1.
PROBLEM 1
We first note, that the function (x) can be written in terms of its Fourier transform as
Z
dk
eikx (k).
(x) =
2
(1)
Similarly, x(x) can
Midterm II Practice (Solutions)
Matthew Poulos
UCLA Department of Physics
(Dated: November 13, 2016)
1.
PROBLEM 1
A particle in an infinte square well has its initial wave funtion an even mixture of the first two stationary states:
(x, 0) = A[1 (x) + 2 (x
Midterm 1 Solutions
Matthew Poulos
UCLA Department of Physics
(Dated: October 26, 2016)
1.
PROBLEM 1
Conservation of momentum requires
hi
= pe cos ,
c
(1)
hf
= pe sin .
c
(2)
Furthermore, conservation of energy requires
hi + mc2 = hf +
p
m2 c4 + p2e c2 .
Quantum Mechanics HW 6 (Solutions)
Matthew Poulos
UCLA Department of Physics
(Dated: November 10, 2016)
1.
PROBLEM 1 - 2.10
The ground state of the harmonic oscillator is given by
0 =
1 x 2
1
e 2 ( )
1/4
(1)
q
~
where = m
is the characteristic length s
Midterm II Practice
1.
A particle in an infinte square well has its initial wave funtion an even mixture of the
first two stationary states:
(x, 0) = A [1 (x) + 2 (x)] .
(a) Normalize (x, 0).
(b) Compute < x > .
(c) If you measure the energy of this part
PHY115A
HW#7
Due 05/30/2016 at discussion session
(Late policy: you will get 80% of credit if you turn in on 06/01/2016, no credit if you turn in
after 12:00 PM 06/03/2016 when the solution will be released and your HW7 will be returned
back to you.)
Quantum Mechanics 115A - Homework # 4
(Due date: May 6, 2016 )
Problem 1 (Griffiths 2.15)
In the ground state of the harmonic oscillator, what is the probability (correct to significant digits)
of finding the particle outside the classically allowed regio
Quantum Mechanics 115A - Homework # 7
(Due date: May 30, 2016)
Problem 1 (Griffiths 2.34)
Consider the step potential
V (x) =
0,
if x 0,
V0 , if x > 0.
(1)
a)
In the case E < V0 , the wave function is in the form of
Aeikx + Beikx , if x 0,
(x) =
F eqx ,
i
Quantum Mechanics 115A - Homework # 2
(Due date: April 22nd, 2016 )
Problem 1 (Griffiths 2.3)
In this problem, we are going to prove that there is no acceptable solution to the time-independent
Shr0dinger equation for infinite square well with E = 0 or E
Quiz
Phy 115 A
2
(x) dx =
Postulate #3 says
Prob(particle is between x and x+dx)
What conclusion can you draw?
A)
(x)
2
dx must
B)
(x)
be exactly =1
2
dx
is finite, but neednt =1
C) (x) 2
must be finite at all x.
D) More than one of these
E) On
Quantum Mechanics 115A - Homework # 6
(Due date: May 20, 2016)
Problem 1 (Griffiths 2.44)
Consider the time-independent Schr
odinger equation for a centered infinite square well with a deltafunction barrier in the middle:
(x), for a < x < a
V (x) =
(1)
,
Quantum Mechanics 115A - Midterm Exam # 1
(Date: April 25th, 2016)
Problem 1
1) Ans: b
The expectation value is the average value of repeated measurements on an ensemble of identically
prepared systems.
2) Ans: b
The Fourier transformation of a delta func
Physics 115A
Fall 2015
T. Tomboulis
Due 10-27-15
HOMEWORK # 4
Reading Assignment: G Ch. 2, sections 2.1, 2.2, 2.4
Problems:
1. Delta function practice
(a) Evaluate the following integrals:
i.
Z +1
dx exp(|x| + 3) (x + 2)
1
ii.
4 Z
X
h
i
dx cos(x) + 2 (2x
Physics 115A
Fall 2015
T. Tomboulis
Due 10-20-15
HOMEWORK # 3
Reading Assignment: G Ch. 2, sections 2.1, 2.2.
Problems:
1. Show that in any stationary state (x, t) = u(x) exp(iEt/
h) we always have:
< p >= 0 .
2. (a) Calculate the averages and standard de
1
Homework #21
A.
Execute the following code in MATLAB, generating spike times for a neuron:
T = 5;
% duration in seconds
time = 0:0.001:T;
% Time in seconds
randomNumbers = rand(1,length(time);
% Random numbers
Threshold = 0.01;
% Threshold
spikeTimesInd
1
Homework1 by Joseph Choi
A.
Generate a matrix B = [1 8 9 0; 2 7 5 2], compute and write the results of the
following expressions and commands:
1. What are the dimensions of the matrix B? 2 x 4
2. What are the dimensions of transpose(B)? 4 x 2
3. What ar
Neurophysics of the Mind
Brain problem
List of readings are posted on the relevant slides
Lecture 1
Physics 186/286
Mayank Mehta
TA: Dr. Karen Safaryan
What is cognitive Neurophysics?
How does the mind arise from the brain
and influence it?
The tale of
Neurophysics of the Mind Brain
problem
Lecture #4
Physics 186/286
Mayank R. Mehta
Neural coding
and perceptual decisions
Britten, K.H., et al., The analysis of visual motion: a comparison of neuronal and psychophysical performance. J Neurosci,
1992. 12(12
Neurophysics of the Mind
Brain problem
Lecture 2
Mayank R. Mehta
Readings for subsequent sections
Reading material related to things discussed
in the class is listed at the bottom of the
relevant pages.
You dont have to read the reading material,
it is
Neurophysics of the Mind
Brain problem
Lecture #3
Physics 186/286
Mayank R. Mehta
Mountcastle, V.B., The columnar organization of the neocortex. Brain,
1997. 120 ( Pt 4): p. 701-22.
Mehta, M.R., Neuronal Dynamics of Predictive Coding. The
Neuroscientist,