Section 3.13: Theorems for Hermitian Operators (under construction) This section discussions some theorems for operators (refer to T. D. Lees Book). The common theorems show when two operators are equal and also discusses alternate methods for determining
Physics 137B (Quantum Mechanics), Spring 2011 Please read this page carefully! Pages 25 are the contents of a text, most of which is written. Pages 6 and 7 oer some advice. Lecturer Charles Wohl, cgwohl@lbl.gov 486-4730, oce hours in 251 Le Conte (the Rea
Harmonic Oscillator: From a and a to the position representation
Michele Kotiuga Physics 137A Spring 2010
In lecture the harmonic oscillator potential was treated using creation and annihilation operators: a and a . In Section 4.7 of Bransden and Joachain
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
Eigenvectors of a Hermitian operator
Formalism of Quantum Mechanics
Dirac Notation We can use a shorthand notation for the normalization integral
I = " ! (r, t ) dr = " ! * (r, t )! (r, t )dr = ! !
2
The state ! is called a ket. The complex conjugate of the ket ! is called a bra More general
1. PARTICLES AND WAVES. THE ATOMIC MODEL
1. Particles and Waves: Neutrons and Light 2. The Bohr Hydrogen Atom: Quantized Energies and Spectra Problems
It will be assumed that the reader has some background in modern physics. This chapter is not meant to b
4. MATHEMATICAL FORMALISM
1. Vector Spaces. Dirac Notation 2. States as Vectors 3. Operators 4. Successive Operations. Commutators 5. Operators as Matrices 6. Expectation Values 7. More Theorems 8. Rules and Interpretations Problems
This chapter needs a l
9. SPIN-1/2 PARTICLES
1. Spinors. Eigenvalues and Eigenstates 2. The Polarization Vector 3. Magnetic Moments and Magnetic Fields 4. Time Dependence. Precessing the Polarization 5. Magnetic Resonance. Flipping the Polarization 6. Stern-Gerlach Experiments