PH3103 : Quantum Mechanics II (Autumn 2012) | Academic Portal of IISER Kolkata

Details of PH3103 (Autumn 2012)

Level: 3

Type: Theory

Credits: 3.0

Course Code	Course Name	Instructor(s)
PH3103	Quantum Mechanics II	Rangeet Bhattacharyya

Syllabus
Recapitulation of basic concepts. The spectral theorem for Hermitian operators. Complete set of commuting observables. Measurement in quantum mechanics. The density operator. Angular momentum. Orbital angular momentum and its connection with spatial rotations. Commutation relations. The eigenspectrum of $J^2$ and $J_z$ . Schroedinger equation for a particle in a central potential. Separation of variables in spherical polar coordinates. Its connection with angular momentum. The hydrogen atom. Reduction to a one body problem. The radial wave function for the Kepler problem. The eigenspectrum of the hydrogen atom. Particle in a spherical well. The isotropic harmonic oscillator. Stern-Gerlach experiment. Spin and total angular momentum. The eigenspectrum of and . Matrix representations of angular momentum operators and rotation matrices. Rotational symmetry and the Wigner-Eckert theorem. The addition of angular momenta. The Clebsch-Gordon Series. Evolution of two coupled angular momenta. The special case of two spin-half particles. The need for approximation methods for time independent Hamiltonians. The variational principle. The WKB approximation. Time independent perturbation theory for a non-degenerate energy level. Time independent perturbation theory for a degenerate energy level. The fine structure of hydrogen. The Zeeman effect and Stark effect.

Syllabus

Recapitulation of basic concepts.

The spectral theorem for Hermitian operators. Complete set of commuting observables. Measurement in quantum mechanics. The density operator.

Angular momentum. Orbital angular momentum and its connection with spatial rotations. Commutation relations. The eigenspectrum of $J^2$ and $J_z$ .

Schroedinger equation for a particle in a central potential. Separation of variables in spherical polar coordinates. Its connection with angular momentum. The hydrogen atom. Reduction to a one body problem. The radial wave function for the Kepler problem. The eigenspectrum of the hydrogen atom. Particle in a spherical well. The isotropic harmonic oscillator.

Stern-Gerlach experiment. Spin and total angular momentum. The eigenspectrum of and . Matrix representations of angular momentum operators and rotation matrices. Rotational symmetry and the Wigner-Eckert theorem.

The addition of angular momenta. The Clebsch-Gordon Series. Evolution of two coupled angular momenta. The special case of two spin-half particles.

The need for approximation methods for time independent Hamiltonians. The variational principle. The WKB approximation. Time independent perturbation theory for a non-degenerate energy level. Time independent perturbation theory for a degenerate energy level. The fine structure of hydrogen. The Zeeman effect and Stark effect.

References
R Shankar, Principles of quantum mechanics, Springer (1994). J. J. Sakurai, Modern quantum mechanics. Pearson Education Inc. (2004). J. S. Townsend, A modern approach to quantum mechanics, University Science Books( 2000) L. E. Ballentine, Quantum mechanics : a modern approach, World Scientific Publishing Company ( 1998). D. J. Griffiths, Introduction to Quantum Mechanics, Pearson Education Inc.(2005).

References

R Shankar, Principles of quantum mechanics, Springer (1994).
J. J. Sakurai, Modern quantum mechanics. Pearson Education Inc. (2004).
J. S. Townsend, A modern approach to quantum mechanics, University Science Books( 2000)
L. E. Ballentine, Quantum mechanics : a modern approach, World Scientific Publishing Company ( 1998).
D. J. Griffiths, Introduction to Quantum Mechanics, Pearson Education Inc.(2005).

Course Credit Options

Sl. No.	Programme	Semester No	Course Choice
1	IP	1	Core
2	IP	3	Not Allowed
3	MS	5	Core
4	RS	1	Not Allowed

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Details of PH3103 (Autumn 2012)

Course Credit Options