Chapter 6
Quantum Theory of the Hydrogen Atom
6.1 Schrdinger's Equation for the Hydrogen Atom
Today's lecture will be all math. Advice: grit your teeth and bear it.
Now that we have discovered a "new" theory (quantum mechanics as exemplified by Schrdinger
Ch 12 Practice MC Problems
1. Which of the following frequencies corresponds to light with the longest wavelength?
A) 3.00 1013 s1
B) 4.12 105 s1
C) 8.50 1020 s1
D) 9.12 1012 s1
E)
3.20 109 s1
2. From the following list of observations, choose the one tha
Physics 505
Homework No. 5
Solutions
S5-1
1. Angular momentum uncertainty relations. A system is in the lm eigenstate of L2 , Lz .
(a) Show that the expectation values of L = Lx iLy , Lx , and Ly all vanish.
Solution
p
hlm | L | lm i = h
l(l + 1) m(m 1)
CHAPTER 4
HANS GEIGER and ERNEST MARSDEN
-suggested by Ernest Rutherford
-disproved JJ Thomsons atomic model which describes that an atom is a like a
fruitcake with raisins which are the electrons. This means that the electric
charges are uniformly spread
Angular momentum in spherical coordinates
We wish to write Lx , Ly , and Lz in terms of spherical coordinates. Recall that the gradient
operator is
~ = rr + 1 + 1 .
r
r sin
You should be able to write this down from a simple geometrical picture of spheri
II
vV\ ~
~tv)
(kep" I C S
,
~V'
~
N\)\ft,d\~
6Mrl u.~rtJ-toV\J>"
\I\h\tj
~e.A~)
B
Angular Momentum in Spherical
Coordinates
In this appendix, we will show how to derive the expressions of the gradient v, the Laplacian
v2, and the components of the orbital
Delta function terms arising from classical point-source fields
Jeffrey M. Bowen
Department of Physics, Bucknell University, Lewisburg, Pennsylvania 17837
(Received 7 June 1993; accepted 28 January 1994)
In the context of classical vector and tensor elds,
examples of the
use of Schrodingers
equaon
In this chapter several examples will be presented to illustrate the use of the
Schrcidinger equation and the application of boundary conditions. In the process
of studying these examples, the physical meaning of
arXiv:1009.2480v2 [physics.class-ph] 1 Dec 2010
Generalized second-order partial derivatives of 1/r
V Hnizdo
National Institute for Occupational Safety and Health,
Morgantown, West Virginia 26505, USA
E-mail: [email protected]
Abstract. The generalized seco
Index notation in 3D
1
Why index notation?
Vectors are objects that have properties that are independent of the coordinate system that
they are written in. Vector notation is advantageous since it is elegant and deals with vectors
as single objects rather
COMMENT ON COMMENT ON SOME NOVEL DELTA-FUNCTION
IDENTITIES BY CHARLES P FRAHM (AM. J. PHYS 51 8269
(1983) BY J. FRANKLIN (AM. J. PHYS 78 122526 (2010)
arXiv:1308.2262v1 [math-ph] 10 Aug 2013
YUNYUN YANG AND RICARDO ESTRADA
Abstract. We prove the formula
VECTORS
AND
MINEMATICSA FEW
MATHEMATICAL
VECTORS AND KINEMATICS-A FEW MATHEMATICAL PRELIMINARIES
1.1 lntroduction
The goal of this book is to help you acquire a deep understanding
of the principles of mechanics. The subject of mechanics is a t
the very he
Princeton University
Ph501
Electrodynamics
Problem Set 1
Kirk T. McDonald
(1998)
[email protected]
http:/puhep1.princeton.edu/~mcdonald/examples/
References:
R. Becker, Electromagnetic Fields and Interactions (Dover Publications, New York, 1982).
D.J.
Lecture 13: More on Gradient; the Operator Del
13. 1. Examples of the Gradient in Physical Laws
Gravitational force due to Earth: Consider the potential energy of a particle of mass
m, a height z above the Earths surface V = mgz. Then the force due to gra
See discussions, stats, and author profiles for this publication at: https:/www.researchgate.net/publication/45894398
Comment on "Some novel delta-function
identities"
Article January 2010
Source: arXiv
CITATIONS
READS
8
45
1 author:
Jerrold Franklin
Temp
6. Velocity and Acceleration
A particle moving in space sweeps out a curve. The position vector
~r(t) = x(t) + y(t)
+ z(t)k = hx(t), y(t), z(t)i,
is naturally a function of time t. For example, the cycloid
~r(t) = ht sin t, 1 cos ti.
The velocity vector
CHECK UP QUIZ NUMBER 1
June 11 2015
Modules 1 and 2
Convert the following to SI units
1. 100 cm/hr
2. 2.59 in3
*Express the following in scientific notation.
3. .000817 m
4. 800 000 000 m/s
Express the answer in the correct number of
significant figures:
Motion in 2 or 3 Dimensions
Average and instantaneous velocity
A point in space P1
at a time t1 can be
represented by a
vector r1.
As observed the
point is moving and
follows a path as
shown in the figure.
Average velocity vector
where
Instantaneous vel
Announcements HW #1 is due next Wednesday by 8am. Textbook
Hobson, "Physics Concepts & Connections" 4th ed Not 100% essential, but it is very useful
Honors Option and overrides Please check corrected reading assignment link to website available in LON-C
Today Announcements:
HW#1 is due Wednesday by 8:00 am The first LONCAPA extra credit assignment is due 1/22 by 8:00 am.
Review from last time Units Scalars, Vectors and Tensors Motion and Newton's Law of Inertia
ISP209s9 Lecture 2 -1-
Review: Einstein'