Exercise 6.6 A particle of mass m moves in the three-dimensional potential V(x, y, z) =...

   

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Exercise 6.6 A particle of mass m moves in the three-dimensional potential V(x, y, z) = { mo²z² for 0 < x <a, 0 <y <a, and z> 0 elsewhere. +∞o, 6.6. EXERCISES 387 it to a set of familiar one-dimensional equations; then find the normalized wave function (a) Write down the time-independent Schrödinger equation for this particle and reduce (x, y, z). Ynynynz (b) Find the allowed eigenenergies of this particle and show that they can be written as: Enynyn = Enxny + En.. (c) Find the four lowest energy levels in the xy plane (i.e., Enny) and their corresponding degeneracies. Problem 1: Exercise 6.16 (page 389) Typo correction: (1) the initial wave function is y(7,0)= A(1) ³. ( 2 1 √12T z-√√2x 2x), (r) (2) (d) the angular operators in question (d) are and £,. (Hint: (1) R. (r) = 2 (1) R. (r) = 2(1-³.. (2) apply Table 5.2. do (3) (nlm|r|n'l'm') = (nlm\r\n'l'm') 5₁mm). Exercise 6.6 A particle of mass m moves in the three-dimensional potential V(x, y, z) = { mo²z² for 0 < x <a, 0 <y <a, and z> 0 elsewhere. +∞o, 6.6. EXERCISES 387 it to a set of familiar one-dimensional equations; then find the normalized wave function (a) Write down the time-independent Schrödinger equation for this particle and reduce (x, y, z). Ynynynz (b) Find the allowed eigenenergies of this particle and show that they can be written as: Enynyn = Enxny + En.. (c) Find the four lowest energy levels in the xy plane (i.e., Enny) and their corresponding degeneracies. Problem 1: Exercise 6.16 (page 389) Typo correction: (1) the initial wave function is y(7,0)= A(1) ³. ( 2 1 √12T z-√√2x 2x), (r) (2) (d) the angular operators in question (d) are and £,. (Hint: (1) R. (r) = 2 (1) R. (r) = 2(1-³.. (2) apply Table 5.2. do (3) (nlm|r|n'l'm') = (nlm\r\n'l'm') 5₁mm).

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Solution a Time independent schrodiger equation for this particle is h 2m Where h 2m Let x y z YZ 7 ... View the full answer