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Consider an electron whose wave function is ?(r,0,?)-- e* sin ? + cos ?)f(r). 47t where...
##### show all steps thoroughly (sorry for my bad grammar) Assume that electron in state have wave function of spherical coordinate 4π Where g(r) wave function in part of radius By (r)|-r-dr = 1)show...
##### show all steps thoroughly (sorry for my bad grammar)
Assume that electron in state have wave function of spherical coordinate 4π Where g(r) wave function in part of radius By (r)|-r-dr = 1)show that wave function write in term of (theta, d) 2)find expectation of L
Assume that electron in state have wave function of spherical coordinate 4π Where g(r) wave function in part of radius By (r)|-r-dr = 1)show that wave function write in term of (theta, d)...
##### show all steps thoroughly (sorry for my bad grammar) Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Fi...
##### show all steps thoroughly (sorry for my bad grammar)
Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Find expectation value of angular momentum squared (L2) 3) Find expectation value of angular momentum in component axis -Z L) 4) How much angular momentum in component axis-Z will probability of found particle? And why?
Assume that electron in area electric field of proton...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0 where N is a real normalization constant and o is a real positive constant with units of (length)-1. For the following, express your answers in terms of a: a) Calculate the momentum space wave function. b) Verify that the momentum space wave function is normalized such that (2.4) c) Use the momentum space wave function to calculate the expectation value (p) via (2.5)
1) Write the following wave functions of the Hydrogen atom b100(r, 0, )= 1s b200(r, 0,...
1) Write the following wave functions of the Hydrogen atom b100(r, 0, )= 1s b200(r, 0, ) 2s; b21+1(r,0, )= b2p 2) Calculate the medium radius and possible radius for this functions. 3) What are the energy at each state? 4) Calculate the angular momentum of each state using the differential operator 1 L2 h2 1 sin sin2 0 2 sin e ae 5) Verify the above results with the equation L2nlm = l( 1)h2bn{m 6) Calculate the components L2...
5. Part 1. (6 pt) An electron moves around a 2D ring with ring radius 0.50 nm in the state m --20...
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...
Consider a particle confined to one dimension and positive z with the wave function 0 where...
Consider a particle confined to one dimension and positive z with the wave function 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: f) Calculate the expectation value of the momentum, (p) via the canonical expression -0o g) Calculate the expectation value of (p) via the canonical expression h) Use your results for(i) and (pay to calculate the variance in...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2 4 A 3 xz (x, y, z) = 2 2 Calculate L2 (x, y, z) and L-y(x, y, z). Find the total angular momentum of this particle. (b) Calculate L+ y (x, y, z) and (Y L+ W). (c)If a measurement of the z-component of the orbital angular momentum is carried out, find the probabilities corresponding to finding the results 0, h, and -h....
part (e),(f) and (g) 3. Wave functions (40 marks) Consider particle described by wave function (x)...
part (e),(f) and (g)
3. Wave functions (40 marks) Consider particle described by wave function (x) = Ce-x/a for x > 0, and otherwise (C is a real and non-negative). (a) Normalise (x) and plot it (you can use a computer to plotit). (b) Calculate the probability that the particle is located within distance a from the origin. (e) Find mean value of position measurement. (d) Find mean value of momentum measurement. Hint: use the fact that (x) is purely...
Consider the function r 2 cos(6) + sin(26) θ (a) By looking at the Cartesian graph, where is r 0? (For 0 21. Enter your answer using interval notation.) (b) Explain why quadrants Il and Ill of the po...
Consider the function r 2 cos(6) + sin(26) θ (a) By looking at the Cartesian graph, where is r 0? (For 0 21. Enter your answer using interval notation.) (b) Explain why quadrants Il and Ill of the polar graph are empty (c) How many values of θ for 0 θ satisfy r= 1? (d) The polar graph intersects the unit circle 4 times. Explain the discrepancy with you answer to part (c).
Consider the function r 2 cos(6) +...
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where...
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where = -1 1 a 1 22 sin + sin 020 sin0 and derive the corresponding eigenvalues. You may use the identity 1 a 1 sin sin 2 sin sin 0 80 sino 31 (sin 00 (5 marks) (6) Consider the function $(,0,4)= A - 1/200 sin 6e-ip, 20 where A is a constant and an is the Bohr radius. This is a hydrogen atom...
##### show all steps thoroughly (sorry for my bad grammar)
Assume that electron in state have wave function of spherical coordinate 4π Where g(r) wave function in part of radius By (r)|-r-dr = 1)show that wave function write in term of (theta, d) 2)find expectation of L
Assume that electron in state have wave function of spherical coordinate 4π Where g(r) wave function in part of radius By (r)|-r-dr = 1)show that wave function write in term of (theta, d)...
##### show all steps thoroughly (sorry for my bad grammar)
Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Find expectation value of angular momentum squared (L2) 3) Find expectation value of angular momentum in component axis -Z L) 4) How much angular momentum in component axis-Z will probability of found particle? And why?
Assume that electron in area electric field of proton...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0 where N is a real normalization constant and o is a real positive constant with units of (length)-1. For the following, express your answers in terms of a: a) Calculate the momentum space wave function. b) Verify that the momentum space wave function is normalized such that (2.4) c) Use the momentum space wave function to calculate the expectation value (p) via (2.5)
1) Write the following wave functions of the Hydrogen atom b100(r, 0, )= 1s b200(r, 0, ) 2s; b21+1(r,0, )= b2p 2) Calculate the medium radius and possible radius for this functions. 3) What are the energy at each state? 4) Calculate the angular momentum of each state using the differential operator 1 L2 h2 1 sin sin2 0 2 sin e ae 5) Verify the above results with the equation L2nlm = l( 1)h2bn{m 6) Calculate the components L2...
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...
Consider a particle confined to one dimension and positive z with the wave function 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: f) Calculate the expectation value of the momentum, (p) via the canonical expression -0o g) Calculate the expectation value of (p) via the canonical expression h) Use your results for(i) and (pay to calculate the variance in...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2 4 A 3 xz (x, y, z) = 2 2 Calculate L2 (x, y, z) and L-y(x, y, z). Find the total angular momentum of this particle. (b) Calculate L+ y (x, y, z) and (Y L+ W). (c)If a measurement of the z-component of the orbital angular momentum is carried out, find the probabilities corresponding to finding the results 0, h, and -h....
part (e),(f) and (g)
3. Wave functions (40 marks) Consider particle described by wave function (x) = Ce-x/a for x > 0, and otherwise (C is a real and non-negative). (a) Normalise (x) and plot it (you can use a computer to plotit). (b) Calculate the probability that the particle is located within distance a from the origin. (e) Find mean value of position measurement. (d) Find mean value of momentum measurement. Hint: use the fact that (x) is purely...
Consider the function r 2 cos(6) + sin(26) θ (a) By looking at the Cartesian graph, where is r 0? (For 0 21. Enter your answer using interval notation.) (b) Explain why quadrants Il and Ill of the polar graph are empty (c) How many values of θ for 0 θ satisfy r= 1? (d) The polar graph intersects the unit circle 4 times. Explain the discrepancy with you answer to part (c).
Consider the function r 2 cos(6) +...
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where = -1 1 a 1 22 sin + sin 020 sin0 and derive the corresponding eigenvalues. You may use the identity 1 a 1 sin sin 2 sin sin 0 80 sino 31 (sin 00 (5 marks) (6) Consider the function $(,0,4)= A - 1/200 sin 6e-ip, 20 where A is a constant and an is the Bohr radius. This is a hydrogen atom...
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