###### Learning Outcomes:

On completion of this module students should be have complete picture of quantum physics, and be able to apply fundamental quantum mechanics to physical systems. They should have an appreciation of how these theoretical models relate to experimentally determined quantities, and about edge applications of quantum physics.

###### Indicative Module Content:

The time-dependent Schrodinger equation

The probability density and the probability current

The normalization of the wavefunction

The time-independent Schrodinger equation and stationary solutions

Energy eigenstates and eigenfunctions

Orthonormal basis

Wavefunctions as linear combination of eigenfunctions and their time evolution

Expectation values

Energy eigenstates in one dimension

The variational principle (with few examples)

Vector representation of wavefunctions

Position and momentum operators, eigenstates and eigenfunctions

Matrix representations of the position and momentum operators

Momentum representation (Fourier transforms)

Overview of linear algebra (e.g. hermitian and unitary operators, complex vector space) Bra and Ket notation, and inner product

The Stern-Gerlach experiment (complete derivation)

Spin one-half states and operators, vector and matrix representations

Pauli matrices

Spin states in arbitrary directions

Quantum dynamics

Schrodinger dynamics representation

Unitary time evolution operator

Derivation of the Schrodinger equation

Derivation of the unitary time evolution operator

Heisenberg dynamics representation

Heisenberg operators and equation of motion

Examples of Schrodinger and Heisenberg representations (e.g. harmonic oscillator)

Two state systems case and the vector representation of the Schrodinger equation

Spin precession in a magnetic field

The ammonia molecule

Ammonia molecule in an electric field, and the MASER (Nobel Prize work)

Nuclear Magnetic Resonance and Magnetic Resonance Imaging (Nobel Prize work)

Multiparticle states and tensor product

Entangled states

Bell basis states

Quantum teleportation

EPR paradox

Bell Inequality

Introduction to quantum information theory

Introduction to quantum biology

Time dependent perturbation theory

Scattering theory, and neutron scattering

Dirac equation