Page 1 Multiple Choice Questions in Basic Quantum Mechanics 1 1 Module 10: Time Independent Perturbation Theory 10.1 Consider a 4-fold degenerate state with orthonormal eigenfunctions 1 2 3 4 , , and u u u u . There is a perturbationH . It is given that 12 21 ;0 H H g g and all the other matrix elements are zero. Find the splitting and corresponding wavefunctions. (a) , ,0,0 gg (b) 2 , ,0,0 gg (c) , ,0,0 gg (d) ,0,0,0 g [Answer (a)] 10.2 Consider a 4-fold degenerate state with orthonormal eigenfunctions 1 2 3 4 , , and u u u u . There is a perturbationH . It is given that 12 21 ;0 H H g g , and all the other matrix elements are zero. Find the wave functions of the split levels. (a) 1 2 3 4 , , and u u u u (b) 1 2 1 2 34 , , and 22 u u u u uu (c) 1 2 1 2 34 22 , , and 22 u u u u uu (d) 1 2 1 2 34 33 , , and 22 u u u u uu [Answer (b)] 10.3 Consider a 4-fold degenerate state with orthonormal eigenfunctions 1 2 3 4 , , and u u u u . There is a perturbationH . It is given that 11 22 2 H H g , 12 21 H H g and all the other matrix elements are zero. Find the splitting and corresponding wavefunctions. (a) , ,0,0 gg (b) 2 , ,0,0 gg (c) 3 , ,0,0 gg (d) 4 , ,0,0 gg [Answer (c)] Page 2 Multiple Choice Questions in Basic Quantum Mechanics 1 1 Module 10: Time Independent Perturbation Theory 10.1 Consider a 4-fold degenerate state with orthonormal eigenfunctions 1 2 3 4 , , and u u u u . There is a perturbationH . It is given that 12 21 ;0 H H g g and all the other matrix elements are zero. Find the splitting and corresponding wavefunctions. (a) , ,0,0 gg (b) 2 , ,0,0 gg (c) , ,0,0 gg (d) ,0,0,0 g [Answer (a)] 10.2 Consider a 4-fold degenerate state with orthonormal eigenfunctions 1 2 3 4 , , and u u u u . There is a perturbationH . It is given that 12 21 ;0 H H g g , and all the other matrix elements are zero. Find the wave functions of the split levels. (a) 1 2 3 4 , , and u u u u (b) 1 2 1 2 34 , , and 22 u u u u uu (c) 1 2 1 2 34 22 , , and 22 u u u u uu (d) 1 2 1 2 34 33 , , and 22 u u u u uu [Answer (b)] 10.3 Consider a 4-fold degenerate state with orthonormal eigenfunctions 1 2 3 4 , , and u u u u . There is a perturbationH . It is given that 11 22 2 H H g , 12 21 H H g and all the other matrix elements are zero. Find the splitting and corresponding wavefunctions. (a) , ,0,0 gg (b) 2 , ,0,0 gg (c) 3 , ,0,0 gg (d) 4 , ,0,0 gg [Answer (c)] Multiple Choice Questions in Basic Quantum Mechanics 2 2 10.4 Consider a 4-fold degenerate state with orthonormal eigenfunctions 1 2 3 4 , , and u u u u . There is a perturbationH . It is given that 11 22 2 H H g , 12 21 H H g and all the other matrix elements are zero. Find the wave functions of the split levels. (a) 1 2 3 4 , , and u u u u (b) 1 2 1 2 34 , , and 22 u u u u uu (c) 1 2 1 2 34 22 , , and 22 u u u u uu (d) 1 2 1 2 34 33 , , and 22 u u u u uu [Answer (b)]Read More

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