Motivations for studying quantum mechanics – Basic principles of quantum mechanics,Probabilities and probability amplitudes – Linear vector spaces , bra and ket vectors – Completeness, orthonormality, basis vectors – Orthogonal, Hermitian and Unitary operators, change of basis.
Eigenvalues and expectation values, position and momentum representation – Measurement and the generalized uncertainty principle – Schrodinger equation, plane wave solution – Probability density and probability current – Wavepackets and their time evolution – Ehrenfest relations – 1-dimensional potential well problems, particle in a box – Tunnelling through a potential barrier – The linear harmonic oscillator; Operator approach – The linear harmonic oscillator and the Hermite polynomials.
Coherent states and their properties. Application to optics – Other interesting superpositions of basis states such as squeezed light – Motion in 3-dimensions; The central potential problem – Orbital angular momnetum and spherical harmonics – Hydrogen atom ; its energy eigenvalues and eigenfunctions – Additional symmetries of the hydrogen atom – The deuteron ; Estimation of the size of the deuteron – The isotropic oscillator, energy degeneracy – Invariance principles and conservation laws – Spin and the Pauli matrices – Addition of angular momentum – The spin-orbit coupling and its consequences.
Charged particle in a uniform magnetic field; Energy eigenvalues and eigenfunctions – The Schrodinger, and Heisenberg pictures, Heisenberg equations of motion – The interaction picture – The density operator; pure and mixed states, with examples – An introduction to perturbation theory; its relevance, and physical examples – Time-independent perturbation theory : non-degenerate case – Time-independent perturbation theory:degenerate case – Time- dependent perturbation theory; atom- field interactions and the dipole approximation – Examples of time-dependent calculations – Summary of non-classical effects surveyed in the course
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