Duality of radiation and matter, De broglie’s hypothesis, justification for the relation, Experimental confirmation of l = h/p (Davission and Germer experiment).

Uncertainty principle relating to position and momentum, relating to energy and time, its applications to various quantum mechanical problems such as:

(i)             Non-existence of electrons in nucleus

(ii)           Ground state energy of H-atom

(iii)          Ground state energy of Harmonic oscillator

(iv)          Natural width of spectral line

Schrodinger equation:

Wave function and its interpretation, Schrödinger time dependent and time independent one-dimensional equation, three-dimensional  Schrödinger wave equation, probability current density, physical meaning of  ψ, conditions to be satisfied by  ψ.

Operators, algebra of operators, commutative property, linear operators, Commutator operator, eigen values and eigen functions, operators for momentum, K.E., Hamiltonian, total energy and angular momentum, Fundamental postulates of Q.M.

Hermitian operators, orthonormality, degeneracy, Commutation relations, Ehrenfest’s theorem, Bohr’s principle of complementarity, principle of superposition.

Boundary  and continuity conditions on the wave function. Particle in one dimensional box, eigen function and eigen values, discrete energy levels, generalization to 3-D and degeneracy of levels

Boundary value problems:                                                                                                 

Step potential, Penetration through rectangular barrier, calculation of reflection and transmission coefficients. Quantum mechanical  tunneling. Square well potential problem, reflection and transmission coefficient and resonant scattering.

(1-D Case): Schrödinger equation and its solutions, eigen function, energy eigen values. Zero point energy, parity, symmetric and anti-symmetric wave functions with graphical representation.

 Rigid rotator: Schrodinger equation and its solution.

Introduction: orbital angular momentum,Operators for its Cartesian components, commutation relations, mutual as well as with L² ,L⁺ and L^- operators , their interpretation as step operators, eigen values of L_z, Total angular momentum operators, commutation relations obeyed by the components of generalized momentum operator. Commutation relation of  J_z with J₊ and J_- , J₊ and J_- ,commutation relation of J² with J₊ and J_-.