Question

5. Part 1. (6 pt) An electron moves around a 2D ring with ring radius 0.50 nm in the state m --20. Determine the wavelength (in nm) of the particle wave induced by this electron. (similar to a question in Exam 1) Part 2. (a) (7pt) A wavefunction is given by y, (e, 4-B sin cos(6). Can this function be an eigenfunction of Legendrían operator (A2.sunagatsineaesin暘for a quantum particle moving around a spherical surface)? If so, determine the eigenvalue and the corresponding angular momentum qua ntum number I. (b) (5pt) Can the above wavefunction be an eigenfunction of the z-component angular momentum operator A d ). If so, determine the eigenvalue and the corresponding quantum number m (from Exam 1). 3) s.cs ; Sonm Mı ㄷ-20A+?C.., 5. Part 1" (6 pt) An electron moves around a 2D ring with ring radius-oso nm in the state m .-20. Determine the wavelength (in nm) of the particle wave induced by this electron. (similar to a question in Exam 1) Part 2, (a) (7pt) A wavefunction is given by (9, ф)-B sin cos(6) Can this function be an eigenfunction of (A2 sinzgao-+ s n®aesinθα for a quantum particle moving around a spherical surface)? If so, determine the eigenvalue and the corresponding angular momentum quantum number I (b) (5pt) Can the above wavefunction be an eigenfunction of the z-component angular momentum operator ( dg) If so, determine the eigenvalue and the corresponding quantum number m (from Exam 1). 5. Part 1" (6 pt) An electron moves around a 2D ring with ring radius-oso nm in the state m .-20. Determine the wavelength (in nm) of the particle wave induced by this electron. (similar to a question in Exam 1) Part 2, (a) (7pt) A wavefunction is given by (9, ф)-B sin cos(6) Can this function be an eigenfunction of (A2 sinzgao-+ s n®aesinθα for a quantum particle moving around a spherical surface)? If so, determine the eigenvalue and the corresponding angular momentum quantum number I (b) (5pt) Can the above wavefunction be an eigenfunction of the z-component angular momentum operator ( dg) If so, determine the eigenvalue and the corresponding quantum number m (from Exam 1).

Answer 1

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