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##### PHYSICS 851 - Quantum Mechanics - Michigan State University Study Resources
• 3 Pages
###### 851HW13_09

School: Michigan State University

Course: Quantum Mechanics

PHYS851 Quantum Mechanics I, Fall 2009 HOMEWORK ASSIGNMENT 13 Topics Covered: Spin Please note that the physics of spin-1/2 particles will gure heavily in both the nal exam for 851, as well as the QM subject exam. Spin-1/2: The Hilbert space of a spin-1/2

• 3 Pages
###### Lect29_CentralPot

School: Michigan State University

Course: Quantum Mechanics

Lecture 29: Motion in a Central Potential Phy851 Fall 2009 Side Remarks Counting quantum numbers: 3N quantum numbers to specify a basis state for N particles in 3-dimensions It will go up to 5N when we include spin When does it work: All of the stand

• 3 Pages
###### Lect28_TwoBodyProb

School: Michigan State University

Course: Quantum Mechanics

Lecture 28: The Quantum Two-body Problem Phy851 Fall 2009 Two interacting particles Consider a system of two particles with no external fields By symmetry, the interaction energy can only depend on the separation distance: rr P12 P22 H= + + V R1 R2 2 m1

• 3 Pages
###### Lect27_OrbAngMom

School: Michigan State University

Course: Quantum Mechanics

Lecture 27: Orbital Angular Momentum Phy851 Fall 2009 The General Theory of Angular Momentum Starting point: Assume you have three operators that satisfy the commutation relations: [ J x , J y ] = ihJ z [ J y , J z ] = ihJ x [ J z , J x ] = ihJ y Let: 2

• 3 Pages
###### Lect26_AngMom2

School: Michigan State University

Course: Quantum Mechanics

Lecture 26: Angular Momentum II Phy851 Fall 2009 The Angular Momentum Operator The angular momentum operator is defined as: rrr L = R P It is a vector operator: r r r r L = Lx e x + L y e y + Lz e z According to the definition of the crossproduct, the

• 3 Pages
###### Lect25_AngMom1

School: Michigan State University

Course: Quantum Mechanics

Lecture 25: Introduction to the Quantum Theory of Angular Momentum Phy851 Fall 2009 Goals 1. Understand how to use different coordinate systems in QM (cartesian, spherical,) 2. Derive the quantum mechanical properties of Angular Momentum Use an algebraic

• 3 Pages
###### Lect24_TensorProduct

School: Michigan State University

Course: Quantum Mechanics

Lecture 24: Tensor Product States Phy851 Fall 2009 Basis sets for a particle in 3D Clearly the Hilbert space of a particle in three dimensions is not the same as the Hilbert space for a particle in one-dimension In one dimension, X and P are incompatible

• 3 Pages
###### Lect23_HeisUncPrinc

School: Michigan State University

Course: Quantum Mechanics

Lecture 23: Heisenberg Uncertainty Principle Phy851 Fall 2009 Heisenberg Uncertainty Relation Most of us are familiar with the Heisenberg Uncertainty relation between position and momentum: h x p 2 How do we know this is true? Are the similar relations

• 3 Pages
###### Lect22_CohStates

School: Michigan State University

Course: Quantum Mechanics

Lecture 22: Coherent States Phy851 Fall 2009 Summary Properties of the QM SHO: memorize P2 1 H= + m 2 X 2 2m 2 A= = h m 1 X 1 X i P + i P A = h h 2 2 (A + A ) P = i h A A X= 2 2 ( ) 1 H = h A A + 2 H n = h (n + 1 / 2) n A n = n n 1 A n = n + 1 n + 1 n=

• 3 Pages
###### Lect4_BasisSet

School: Michigan State University

Course: Quantum Mechanics

Hermitian Operators Definition: an operator is said to be Hermitian if it satisfies: A=A Alternatively called self adjoint In QM we will see that all observable properties must be represented by Hermitian operators Theorem: all eigenvalues of a Hermitia

• 3 Pages
###### Lect3_Operators

School: Michigan State University

Course: Quantum Mechanics

Operators In QM, an operator is an object that acts on a ket, transforming it into another ket Let A represent a generic operator An operator is a linear map A:HH A|= | Operators are linear: A(a |1+b |2) = aA |1+bA|2 a and b are arbitrary c-numbers No

• 4 Pages
• ###### Evolution In Time Notes
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###### Evolution In Time Notes

School: Michigan State University

Course: Quantum Mechanics

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• 11 Pages
###### Lect31_DipoleMoments

School: Michigan State University

Course: Quantum Mechanics

Lecture 31: The Hydrogen Atom 2: Dipole Moments Phy851 Fall 2009 Electric Dipole Approximation The interaction between a hydrogen atom and an electric field is given to leading order by the Electric Dipole approximation: rr VE = D E (rCM ) `Semi-Classica

• 3 Pages
• ###### Electromagnetic Field Notes
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###### Electromagnetic Field Notes

School: Michigan State University

Course: Quantum Mechanics

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• 5 Pages
• ###### Adding Angular Momentum Notes
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School: Michigan State University

Course: Quantum Mechanics

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• 5 Pages
• ###### Time-Dependent Interactions Notes
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###### Time-Dependent Interactions Notes

School: Michigan State University

Course: Quantum Mechanics

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• 4 Pages
###### Fermions Notes

School: Michigan State University

Course: Quantum Mechanics

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• 3 Pages
• ###### Wigner-Eckart Theorem Notes
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###### Wigner-Eckart Theorem Notes

School: Michigan State University

Course: Quantum Mechanics

& r q g H3 H3 H3 Gr 3@kq g x " x y#G v x i3# x " z x " " z iiytyw!qbDiRvy#tyxs v y#" #vqy00y#" 3 x x " z z x " x wyi0x3D80q001 v #" 1'#" v 'x# v #y3siX x z x " \$ y ! x ! x x " " " x z x 9 Q 7 5 t 5 5 U B Q I P1e8eR)t @P@V@VU 5 a Q f 7U Y 7 r q & 3 % Rq 0P

• 11 Pages
###### Lect30_Hydrogen

School: Michigan State University

Course: Quantum Mechanics

Lecture 30: The Hydrogen Atom Phy851 Fall 2009 Example 2: Hydrogen Atom The Hamiltonian for a system consisting of an electron and a proton is: Pp2 Pe2 e2 H= + rr 2me 2m p 4 0 Re R p In COM and relative coordinates, the Hamiltonian is separable: H = H C

• 1 Page
###### syllabus

School: Michigan State University

Course: Quantum Mechanics

PHYS 851 Quantum Mechanics I Fall Quarter 2008 Class Hours: MWF 10:20 AM to 11:10 AM Class Location: 1415 BPS Textbook: Quantum Mechanics, Volume One, Claude Cohen-Tannoudji Webpage: http:/www.pa.msu.edu/mmoore/851.html Instructor: Prof. Michael Moore Oce

• 1 Page
###### syllabus (1)

School: Michigan State University

Course: Quantum Mechanics

PHYS 851 Quantum Mechanics I Fall Quarter 2009 Class Hours: MWF 10:20 AM to 11:10 AM Class Location: 1420 BPS Textbook: Quantum Mechanics, Volume One, Claude Cohen-Tannoudji Webpage: http:/www.pa.msu.edu/mmoore/851.html Instructor: Prof. Michael Moore Oce

• 3 Pages
###### math_tutorial

School: Michigan State University

Course: Quantum Mechanics

math_tutorial.nb H* This is how you make a comment in Mathematica *L 2 + 2 H* @shiftD + @enterD *L 4 1 In[2]:= In[3]:= In[4]:= Out[4]= In[5]:= H* In mathematica , you type a formula, then hit @shiftD+@enterD to have mathematica evaluate the expression *L

• 18 Pages
###### Lect33_Spin

School: Michigan State University

Course: Quantum Mechanics

Lecture 33: Quantum Mechanical Spin Phy851 Fall 2009 Intrinsic Spin Empirically, we have found that most particles have an additional internal degree of freedom, called spin The Stern-Gerlach experiment (1922): Each type of particle has a discrete numbe

• 3 Pages
###### Lect2_DiracNot

School: Michigan State University

Course: Quantum Mechanics

Lecture I: Dirac Notation To describe a physical system, QM assigns a complex number (`amplitude) to each distinct available physical state. (Or alternately: two real numbers) What is a `distinct physical state? Consider a system with M distinct availab

• 3 Pages
###### Lect1_hbari

School: Michigan State University

Course: Quantum Mechanics

Lecture 1: Demystifying h and i We are often told that the presence of h distinguishes quantum from classical theories. One of the striking features of Schrdinger's equation is the fact that the variable, , is complex, whereas classical theories deal with

• 8 Pages
###### 851HW6_09Solutions

School: Michigan State University

Course: Quantum Mechanics

PHYS851 Quantum Mechanics I, Fall 2009 HOMEWORK ASSIGNMENT 6 1. [10 points] The quantum state of a free-particle of mass, M , at time t is a wave-packet of the form (x, t) = 1 e (5/4)0 ( x x 0 ) 4 +ip0 x/ 2 4 0 , We can safely predict that the width of t

• 2 Pages
###### 851HW6_09

School: Michigan State University

Course: Quantum Mechanics

PHYS851 Quantum Mechanics I, Fall 2009 HOMEWORK ASSIGNMENT 6 1. [10 points] The quantum state of a free-particle of mass, M , at time t is a wave-packet of the form (x, t) = 1 (5/4)0 e ( x x 0 ) 4 +ip0 x/ 2 4 0 , We can safely predict that the width of th

• 9 Pages
###### 851HW5_09Solutions

School: Michigan State University

Course: Quantum Mechanics

PHYS851 Quantum Mechanics I, Fall 2009 HOMEWORK ASSIGNMENT 5 1. In problem 4.3, we used a change of variables to map the equations of motion for a sinusoidally driven two-level system onto the time-independent Rabi model. Here we will investigate how this

• 3 Pages
###### 851HW5_09 (1)

School: Michigan State University

Course: Quantum Mechanics

PHYS851 Quantum Mechanics I, Fall 2009 HOMEWORK ASSIGNMENT 5 1. In problem 4.3, we used a change of variables to map the equations of motion for a sinusoidally driven two-level system onto the time-independent Rabi model. Here we will investigate how this

• 7 Pages
###### 851HW4_Solutions09

School: Michigan State University

Course: Quantum Mechanics

PHYS851 Quantum Mechanics I, Fall 2009 HOMEWORK ASSIGNMENT 4: Solutions 1. The 2-Level Rabi Model: The standard Rabi Model consists of a bare Hamiltonian H0 = and a coupling term V = |1 2| + |2 1|. 2 2 2 (|2 2| |1 1|) (a) What is the energy, degeneracy,

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