Syllabus
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Course Code: EP-703 Course Name: Quantum Mechanics-I |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | General formalism of Quantum Mechanics States and operators; Representation of States and dynamical variables; Linear vector space; Bra Ket notation, Linear operators; Orthonormal set of vectors, Completeness relation; Hermitian operators, their eigenvalues and eigenvectors, The fundamental commutation relation; Schwartz Inequality, Commutation rule and the uncertainty relation; Simultaneous eigenstates of commuting operators; Postulates of quantum mechanics, The unitary transformation; Dirac delta function; Relation between kets and wave functions; Matrix representation of operators; Solution of linear harmonic oscillator problem by operator method (Ladder Operators), Matrix elements of x, p, a, a+ and H; Uncertainty Product for simple harmonic oscillator. |
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| 2 | Angular momentum operator Angular momentum operators and their representation in spherical polar co-ordinates; Eigenvalues and eigenvectors of L2, spherical harmonics; Commutation relations among Lx, Ly, Lz ; Rotational symmetry and conservation of angular momentum; Eigenvalues of J2 and Jz and their matrix representation; Pauli spin matrices; Addition of angular momentum, Clebsch-Gordan coefficients and their calculation for j1= j2 =1/2, j1=1, j2 =1/2 and j1= j2 =1. |
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| 3 | Solution of Schrodinger equation for three dimensional problems The three dimensional harmonic oscillator in both cartesian and spherical polar coordinates, eigenvalues eigenfunctions and the degeneracy of the states; Solution of the hydrogen atom problem, the eigenvalues eigenfunctions and the degeneracy. |
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| 4 | Perturbation Theory Time independent perturbation theory; Non-degenerate case, the energies and wave functions in first order, the energy in second order; Anharmonic perturbations of the form λx3 and λx4; Degenerate perturbation theory; Stark effect on the ground and the first excited state of hydrogen. |
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