### Spring 2023

### Michael Kiessling

### Course Description:

This course introduces the student to the mathematically well-developed parts of Quantum Physics, taught as a theory about an objectively existing world made of material points that move. Topics covered are (a) Non-relativistic quantum mechanics: de-Broglie-Bohm theory, Schroedinger's equation, motion of point particles, electrical Coulomb and gravitational Newton pair interactions, "external" magnetic fields, particle spin and Pauli equation, stability of everyday matter; (b) Relativistic quantum mechanics: electrons and photons, Dirac's equation, Chandrasekhar's theory of white dwarf stars. Mathematical key words: Hilbert space, self-adjoint operators, unitary operators, spectral theory.

### Textbook:

Prof. Kiessling's lecture notes

### Prerequisites:

Linear algebra and advanced calculus; or special permission by the instructor

### **********************************

### Spring 2022

### Sheldon Goldstein

### Course Description:

This is the second part of the two-part course Introduction to Mathematical Physics. It introduces the student to the mathematically well-developed parts of quantum physics and is taught in the spirit of part I (Classical Physics) as a theory about an objectively existing world made of material points that move. Topics will include (as time permits): Hilbert spaces, non-relativistic quantum mechanics, Schrödinger’s equation, particle motion, electrical Coulomb and gravitational Newton pair interactions, external magnetic fields, particle spin and the Pauli equation, self-adjoint operators and one-parameter groups, quantization of simple systems, the quantum theory of measurement, representations of the canonical commutation relations, the harmonic oscillator, angular momentum, the existence of atomic Hamiltonians, scattering theory. relativistic quantum mechanics, Dirac’s equation, the origin of the quantum rules: Born’s rule, quantum probabilities, and operators as observables.

### Textbook:

None

### Prerequisites:

Linear algebra and advanced calculus, 561, or permission of the instructor

### **********************************

Spring 2020 - Michael Kiessling

### Course Description:

This is the second part of the two-part course Introduction to Mathematical Physics. It introduces the student to the mathematically well-developed parts of Quantum Physics and is taught in the spirit of part I (Classical Physics) as an theory about an objectively existing world made of material points that move. Physics topics covered are (a) Non-relativistic quantum mechanics: deBroglie-Bohm theory, Schroedinger's equation, motion of point particles, electrical Coulomb and gravitational Newton pair interactions, "external" magnetic fields, particle spin and Pauli equation, stability of everyday matter; (b) Relativistic quantum mechanics: electrons and photons, Dirac's equation, Chandrasekhar's theory of white dwarf stars. Mathematical key words: Hilbert space, self-adjoint operators, unitary operators, spectral theory.

### Textbook:

Prof. Kiessling's lecture notes

### Prerequisites:

561, real analysis, or permission by the instructor

### Schedule of Sections:

### Previous Semesters:

- Spring 2020 Prof. Kiessling
- Spring 2019 Prof. A. Soffer
- Fall 2017 Prof. Kiessling