Physics 115A, Solution Set 6
1
SHO in Momentum Space
= p2 + 1 m 2 x
The harmonic oscillator Hamiltonian in any representation is H
2 . So lets
2m
2
consider the simple harmonic oscillator in momentum
Physics 115A, Solution Set 1
NC
1
Discrete statistics at the Tour de France
Related to Griffiths section 1.3.1
Suppose were lucky enough to gather all 61 winners of the Tour de France in one
room, ali
Physics 115A
Homework 6
Problem 3.14
Lets apply the generalized uncertainty principle (Equation 3.62) for the case A = x and B =
H = p2 /2m + V :
2
1
2 2
h[
x, H]i
x H
2i
we need the expectation valu
Physics 115A, Solutions to Problem Set 8
1
Hilbert Space
1. Show that the set of all square-integrable functions (that is, the set of functions f (x)
Rb
for which a |f (x)|2 dx is finite on a specifie
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Physics 115A, Solution Set 7
1
From the Square Well to the Delta Well
We can think of the Dirac delta function as the limiting case of a rectangle of unit area as
the height goes to infinity and the w
Physics 115A, Problem Set 5
Due Tuesday, October 27 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths 2.4. Study for the midterm!
1
The 3D Harmonic Oscillator
Next quarter, when
Physics 115A, Problem Set 6
Due Tuesday, November 3 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths Section 2.5, 2.6
1
SHO in Momentum Space
= p2 + 1 m 2 x
The harmonic oscill
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Physics 115A, Solution Set 3
1
E and V for normalizable solutions
Griffiths Problem 2.2:
Show that E must exceed the minimum value of V (x), for every normalizable solution to
the time-independent Sch
Mastery Questions Week #6 Solutions
1. (*) Recall Heisenbergs Uncertainty Principle:
x p
~
2
(a) Order them by how spread out they are
2
(b) (p) is the square root of the probability density P (p) = (
Mastery Questions Week #8 Solutions
1. Nope, its just a list of three numbers
2. Literally any matrix applied to it
3. Normalizing it, taking the cube of its entries, etc
4. You can represent it with
Problem 1.18 In general, quantum mechanics is relevant when the de Broglie
wavelength of the particle in question (/1/ p) is greater than the characteristic size
of the system (d). In thermal equilibr
Midterm exam Part II. Please work all 3 problems. Dont worry if you cant finish, but *do*
move on to!the next part if you get stuck.!
!
1. (28 pts) A particle of mass m is confined in an infinite squa
Practice Midterm problems
Please work using the posted cover sheet, which contains the information you will be provided
for the actual midterm. (If needed, additional integrals will be provided with t
Physics 115A
Practice Midterm
Seth Koren
Problem 1: Half-Harmonic Oscillator
(a) While it is possible to solve this problem by setting up the Schrodinger equation for this
potential and imposing these
Physics 115A, Solution Set 4
Due Tuesday, October 20 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths 2.3
1
Constructing States
Given the explicit solution for the ground state
Phys 219
Midterm Exam
02/12/15
Instructions: Show all work. Write clearly. Number all pages turned in and number
responses by question and part. Make sure your exam has five sides printed (six
questio
Physics 115A, Solutions to Problem Set 9
1
Proof that 0 = 1?
=
Consider a Hermitian operator A with some eigenvector |ai with real eigenvalue a, A|ai
a|ai. Suppose |ai is normalizable and properly no
Practice Final Exam, Physics 115A
Fall 2015
This exam is closed book, closed notes, closed calculators/phones. Please show your work
for full credit. You may make free use of anything on the Useful Fo
Practice Midterm, Physics 115A
This practice midterm contains problems in the spirit of those you will encounter on
the actual midterm. The length of the practice exam has not been carefully calibrate
Practice Midterm, Physics 115A
This practice midterm contains problems in the spirit of those you will encounter on
the actual midterm. The length of the practice exam has not been carefully calibrate
(V Av).
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L5 H578 7M2 Zita/l
2 ' , A ,_ ,_ , _ \
tzxp A Lx: LS'Dgf% ) LX" 3 P3 2P1 - A? Boil)
A '3 A " 1: 4' A km, '
/1 A , /\ _ _
' = l g A /c
Mmfaous
- A ; ' r
V ,4 A 1] 1 f _,/
Practice Midterm Solutions, Physics 115A
Fall 2017
1. [6 points total] Short answers (at most a few sentences each, plus math where needed)
(a) [1 point] Briefly discuss the physical implications of t
Mastery Questions Week #7 Solutions
1. Consider the delta function well potential V (x) =
(x), where is a positive constant
(a) Energy/distance.
(b) Because having energies lower than V1 , V
1
leads