# A11: Quantum Theory - Material for the year 2020-2021

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16 lectures

Quantum theory was born out of the attempt to understand the interactions between radiation, described by Maxwell's theory of electromagnetism, and matter, described by Newton's mechanics.

Although there remain deep mathematical and physical questions at the frontiers of the subject, the resulting theory encompasses not just the mechanical but also the electrical and chemical properties of matter. Many of the key components of modern technology such as transistors and lasers were developed using quantum theory.

In quantum theory particles also have some wave-like properties. This introductory course explores some of the consequences of this culminating in a treatment of the hydrogen atom.

By the end of this course, students will be able to solve the Schroedinger equation in a range of simple situations and understand its significance. In particular they will be able to calculate the energy levels of hydrogen-like atoms. They will also learn the abstract, algebraic formulation of quantum mechanics which complements and sometimes replaces the solution of the Schroedinger equation.

Wave-particle duality; Schrödinger's equation; stationary states; quantum states of a particle in a box (infinite squarewell potential).

Interpretation of the wave function; boundary conditions; probability density and conservation of current; parity.

The one-dimensional harmonic oscillator; higher-dimensional oscillators and normal modes; degeneracy. The rotationally symmetric states of the hydrogen atom with fixed nucleus.

The mathematical structure of quantum mechanics and the postulates of quantum mechanics.

Commutation relations. Heisenberg's uncertainty principle.

Creation and annihilation operators for the harmonic oscillator. Measurements and the collapse of the wave function.

Schrödinger's cat. Angular momentum in quantum mechanics. The particular case of spin-1/2. Particle in a central potential. General states of the hydrogen atom.

B.H. Bransden and C.J Joachain *Quantum Mechanics* (Second edition, Pearson Education Limited, 2000). Chapters 1-4.

P.C.W. Davies and D.S. Betts, *Quantum Mechanics (Physics and its Applications)* (2nd edition, Taylor & Francis Ltd, 1994). Chapters 1,2,4.

R.P Feynman, R.B Leighton, M. Sands *The Feynman Lectures on Physics, Volume 3*, (Addison-Wesley, 1998). Chapters 1,2 (for physical background).

K.C Hannabuss, *An Introduction to Quantum Theory* (Oxford University Press 1997). Chapters 1-4.

A.I.M. Rae, *Quantum Mechanics* (4th Edition, Taylor & Francis Ltd, 2002). Chapters 1-3.