University of Central Florida Department of Physics Fall 2009 PHY 4604 Problem Set # 5 Due: October 30, 2009
Please, read carefully secs. 52. to 5.4 in Libo. Check out all problems in Chap. 5. Hand in the following problems for grading: 1. Libo, 5.18 (aft
22.02 Problem Set 5 Solution Krane 5.1 Solution
Lets take extreme limit of the shell model: assume only the single unpaired nucleon determines
the properties of the nucleus.
(a) 7Li: A=7, Z=3, N=4
There is an unpaired proton at 1p3/2. Spin: 3/2, Pa
PHYSICS 4455 QUANTUM MECHANICS Problem Set 4 due 9/22/2005, in class.
1. Becoming more familiar with operators. Liboff Problem 3.3 Liboff Problem 3.16 2. and in particular, the displacement operator: Liboff Problem 3.4 Liboff Problem 3.17 3. Why is the Sc
1
I. SYLLABUS AND INTRODUCTION
Let us start with a brief overview of the items that will (hopefully) be covered in this course and to give a guideline of what we are trying to learn. Quantum mechanics 560 and 561 are advanced quantum mechanics courses des
PHYSICS 4455 QUANTUM MECHANICS Problem Set 2 due 9/8/2005, in class.
1. Recapping complex variables. Liboff Problem 1.21, without parts (b), (d), (f), (j). 2. Black-body radiation and the photoelectric effect. Liboff Problem 2.1 Liboff Problem 2.14 3. The
Homework Solutions # 1 (Libo Chapter 3)
3.2
No inverse of D. The integral x dx /x = + c; only up to an arbitrary additive constant. No operator which destroys information can have an inverse. I 1 = I . F 1 = multiplication by 1/F (x), except where F (x)
22.02 Problem Set 4 Solution 1. Krane, problem 4.4. What fraction of the time do the neutron and proton in the deuteron spend beyond the range of their nuclear force? Solution: In center of mass spherical coordinate:
h 2 H = r + V NUC (r ) 2
The energy ei
Homework Solutions # 2 (Libo Chapter 4)
4.5
(a) Given in book. (b) | |f = a| , where a = dx f . (c) f | |f . (d) f | | = f | .
4.8
g (x) = where an = 2 a
a
2 a
an sin
n
nx a
dx sin
0
nx 1 x(xa)eikx = a 2i
2 a
a 0
dx (x2 ax) ei(k+
n )x a
ei(k+
n )x a
Now
Spring Term 2003
22.02 Intro. APPLIED NUCLEAR PHYSICS
Problem Set #1
1. Wave Interference: Give a general expression for the amplitude at point, P , as a function of, , in terms of the amplitude, A, of the incoming wave, the distance between the slits,
22.02 Problem Set 6 Solution Krane 3.9 Compute the total binding energy and the binding energy per nucleon.
B( A X) = Zm(1 H) + Nm n m( A X) c 2 Z Z
(a)
[
]
Li : A = 7, Z = 3, N = 4 m( 7 Li) = 7.016003amu
7
m(1 H) = 1.007825amu m n = 1.008665amu 1amu = 93
Spring Term 2003
22.02 Introduction to APPLIED NUCLEAR PHYSICS
Problem Set #4
1. Krane, problem 4.4 (hint: use the known, E = 2.2 M eV , to evaluate the wavenumbers, k1 , k2 .) 2. Show (using ESTIMATES) that the deuteron has no excited states. Estimat
22.02 Problem Set 3 Solution 1.Solution The energy eigenvalue problem for the given system is:
H = E
h2 d 2 H = + V ( x) 2 m dx 2 0 | x |> a V ( x) = V0 | x | a
For bounded particle, the solution is:
1 = Aex x < a 2 = B sin kx or B'cos kx a x a 3 = Ce x
Spring Term 2003 22.02 Introduction to APPLIED NUCLEAR PHYSICS Problem Set #3
1. A particle of mass m0 is just being bound by a one-dimensional potential well of width 2a and depth V0 . What is the minimum value of: V0 6= 0 for an ODD parity eigenfunction
22.02 Problem Set 2 Solution 1. Particle in 1D box a. The Eigenvalue equation within the box is:
h2 2 H n = n = E n n (1 . 1 ) 2m x 2 Since n ( x) = 0 outside the box and it is a continuous function, it should satisfy the flowing
boundary conditions:
n (
Spring Term 2003
22.02 Introduction to APPLIED NUCLEAR PHYSICS
Problem Set #2
1. Particle in 1D box: Consider a free particle moving in box as shown in gure with innite potential bounding the box at x = 0 and x = L.
V(x)
X
X=0 X= L
a. Solve the ener
22.02 Problem Set 1 Solution 1. Wave Interference Solution
S2
b
S1
D
Assume S1 and S2 are two identical sources. Their electric field components at point P can be expressed as: E1 (t ) = E cos t (1)
E 2 (t ) = E cos(t + )
(2)
Ep E1
E2
Use phasor represent
Spring Term 2003
22.02 Introduction to APPLIED NUCLEAR PHYSICS
Problem Set #5
1. Krane, problems 5.1, 5.2, 5.3, 5.6.
Extra credit: 5.5, 5.14. Relate your answer in problem 5.5 to a property you are familiar with from the Deuteron.
Problem solutions, 25 April 20121
D. E. Soper2
University of Oregon
30 April 2012
Problems 5.20 and 5.21 were pretty simple, so I do not write out the solutions,
but here is a solution for problem 5.12.
Problem 5.12 We are asked to nd the eigenvalues of t
Problem solutions, 18 April 20121
D. E. Soper2
University of Oregon
27 April 2012
Problem 5.1 is pretty simple, so I do not write out the solutions.
Problem 5.2 The probability to nd the unperturbed eigenstate k (0) in
the exact eigenstate k() is
P =
| k
Problem solutions, 9 May 20121
D. E. Soper2
University of Oregon
16 May 2012
Here is a solution for problem 5.38, which seemed to cause the most diculty.
Please check the algebra: there could be errors.
Problem 5.38 With a potential V0 cos(kz t), we write
Problem solutions, 2 May 20121
D. E. Soper2
University of Oregon
9 May 2012
Here is a solution for problem 5.22, which seemed to cause the most diculty.
Problem 5.22 The expectation value of x is
t
x(t) = i 0 xI (t)
t
d VI ( ) 0 + i 0
0
d VI ( )xI (t) 0
.
QM1 Problem Set 1 solutions Mike Saelim
If you nd any errors with these solutions, please email me at [email protected]
1 (a) We can assume that the function is smooth enough to Taylor expand:
cn An .
f (A) =
n
The rest is a straightforward evaluation,
Errata: Typographical Errors, Mistakes, and Comments
Modern Quantum Mechanics, 2nd Edition
J.J. Sakurai and Jim Napolitano
Jim Napolitano
[email protected]
December 9, 2013
Page 2. Figure 1.1. The gure has the north pole on top and the south pole below, reve
Physics 70007, Fall 2009
Answers to HW set #2
October 16, 2009
1. (Sakurai 1.2)
Suppose that a 2x2 matrix X (not necessarily Hermitian, or unitary) is written as
X = a0 + a
where a0 and a1,2,3 are numbers.
(a) How are a0 and ak (k = 1, 2, 3) related to tr
Decay width calculation1
D. E. Soper2
University of Oregon
21 May 2012
Abstract
I oer here a solution for exercise 12.1 in the notes on time dependent perturbation theory.
1
Problem setup
We need to calculate
dk 2(E2 + E1 )
=
1, 0, 0; k, V 2, 1, m; 0
2
.