PH-305 Quantum Mechanics-I 

  1. Historical motivation: wave-particle duality, photo-electric effect, instability of atoms, black body catastrophe.
  2. Observables and operators, postulates of mechanics, measurement problems, the state function and expectation values, Schrödinger wave equation.
  3. Time-independent Schrödinger equation and one-dimensional problems, stationary states, superposition principle, free particles, infinite and finite square well, harmonic oscillator, and delta-function potential.
  4. Hilbert space, Dirac notation, linear transformations, discrete and continuous basis vectors, hermitian and unitary operators.
  5. Compatible observables, commutators, uncertainty principle, minimum uncertainty states.
  6. Time development of state functions, symmetries and conservation laws, conservation of parity, operators for time and space translations.
  7. Waves incident on potential barrier, reflection and transmission coefficients, WKB method.
  8. Quantum mechanics in three-dimensions, cartesian and spherical forms of Schrodinger equation, separation of variables.
  9.  Rotational symmetry, angular momentum as a generator of rotations, spherical harmonics and their properties. Completeness and orthonormality properties.


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