Page 32 - CatalogNEP-PS

 find solution to Schrödinger‘s equation for many systems such as particle in a box,
Hydrogen Atom and familiarize with different quantum numbers.

THEORY (45 Hours)

UNIT 1 (15 Hours)
Planck‘s quantum, Planck‘s constant and light as a collection of photons; Photo-electric effect and
Compton scattering. De Broglie wavelength and matter waves; Davisson-Germer experiment.
Heisenberg uncertainty principle- impossibility trajectory; estimating minimum energy of a
confined principle; Energy-time uncertainty principle. Wave-particle duality. Matter waves and
wave amplitude; Schrodinger equation for non-relativistic particles;
Momentum and Energy operators; stationary states; physical interpretation of wave function,
probabilities and normalization; Probability and probability current densities in one dimension.
Time dependent Schrodinger equation: Time dependent Schrodinger equation and dynamical
evolution of a quantum state; Properties of Wave Function. Interpretation of Wave Function
Probability and probability current densities in three dimensions; Conditions for Physical
Acceptability of Wave Functions. Normalization. Linearity and Superposition Principles.
Eigenvalues and Eigenfunctions. Position, momentum and Energy operators; commutator of
position and momentum operators; Expectation values of position and momentum. Wave
Function of a Free Particle.
Time independent Schrodinger equation-Hamiltonian, stationary states and energy eigenvalues;
expansion of an arbitrary wavefunction as a linear combination of energy eigenfunctions; General
solution of the time dependent Schrodinger equation in terms of linear combinations of stationary
states; Application to spread of Gaussian wave-packet for a free particle in one dimension; wave
packets, Fourier transforms and momentum space wavefunction; Position-momentum uncertainty
principle.
UNIT 2 (15 Hours)

General discussion of bound states in an arbitrary potential- continuity of wave function,
boundary condition and emergence of discrete energy levels; application to one-dimensional
problem-square well potential; Quantum mechanics of simple harmonic oscillator-energy levels
and energy eigenfunctions using Frobenius method; Hermite polynomials; ground state, zero point
energy & uncertainty principle.
One dimensional infinitely rigid box- energy eigenvalues and eigenfunctions, normalization;
Quantum dot as an example; Quantum mechanical scattering and tunnelling in one dimension -
across a step potential and across a rectangular potential barrier.
UNIT 3 (15 Hours)

Quantum theory of hydrogen-like atoms: time independent Schrodinger equation in spherical
polar coordinates; separation of variables for second order partial differential equation; angular
momentum operator & quantum numbers; Radial wavefunctions from Frobenius method; shapes
of the probability densities for ground & first excited states; Orbital angular momentum quantum
numbers l and m; s, p, d,.. shells.
Atoms in Electric & Magnetic Fields: Electron angular momentum. Space quantization. Electron
Spin and Spin Angular Momentum. Larmor‘s Theorem. Spin Magnetic Moment. Stern-Gerlach
Experiment. Zeeman Effect: Electron Magnetic Moment and Magnetic Energy, Gyromagnetic
Ratio and Bohr Magneton. Atoms in External Magnetic Fields: Normal and Anomalous Zeeman
Effect. Paschen Back and Stark Effect (Qualitative Discussion only).
Many electron atoms: Pauli‘s Exclusion Principle. Symmetric & Antisymmetric Wave Functions.
Periodic table. Fine structure. Spin orbit coupling. Spectral Notations for Atomic States. Total
angular momentum. Vector Model. Spin-orbit coupling in atoms-L-S and J-J couplings. Hund‘s
Rule. Term symbols. Spectra of Hydrogen and Alkali Atoms (Na etc.).

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