In an infinite square well , probabilities for the ground state, n=1,. Consider now the n=3...
In an infinite square well , probabilities for the ground state,
n=1,. Consider now the n=3 state (
(x)n=3
is shown in fig. 6-4). Between 3L/8 and 5L/8, what is the
probability of finding the electron?
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In an infinite square well , probabilities for the ground state,
n=1,. Consider now the n=3...
A particle is in the ground state of a symmetric infinite square well with Vx) O...
A particle is in the ground state of a symmetric infinite square well with Vx) O for -a/2<x<+a/2, and infinite elsewhere. (a) The well then undergoes an instantaneous symmetric expansion to -a <<< ta. Calculate the probabilities of the particle being found in each of the three lowest energy states of the larger well. (b) Instead, suppose that the well expansion takes place adiabatically. Again, calculate the probabilities of the particle being found in each of the three lowest energy...
4) (2096) For an electron in a one-dimensional infinite square well of width L, find (a)...
4) (2096) For an electron in a one-dimensional infinite square well of width L, find (a) (5%) < x >, (b) (5%) < x2 >, and (c) (5%) Δ). (d) (5%) What is the probability of finding the electron between x = 0.2 L and x = 0.4 L if the electron is in n=5 state
5) A particle of mass m is in the ground state of the infinite square well...
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny, and n, are integers. The corresponding allowed en...
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny, and n, are integers. The corresponding allowed energies are Now let us introduce the perturbation otherwise a) Find the first-order correction to the ground state energy b) Find the first-order correction to the first excited state
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny,...
6. Show that for an infinite square well (p2-CanE), and compute (p2〉 for the ground state.
6. Show that for an infinite square well (p2-CanE), and compute (p2〉 for the ground state.
6. Show that for an infinite square well (p2-CanE), and compute (p2〉 for the ground state.
Consider the electron states in an infinite square well potential. a) If the difference in energy...
Consider the electron states in an infinite square well potential. a) If the difference in energy between the n=2 and the n=3 states is 2 eV, calculate the width of this square well. b) If energy making a transition from the n=3 state to the n=2 state gives up the energy difference as an emitted photon, what is the wavelength of the photon?
6. (a) Consider the infinite square well again. Let the width of the well be a...
6. (a) Consider the infinite square well again. Let the width of the well be a and the particle mass be m. Find an expression for the probability that a particle in the state, vi will be found in the region a/4 <x<3a/4. (b) Repeat part (a) for the nth eigenstate, yn, for arbitrary n. Show that the answer reduces to the classical value of 2 as n 00.
6. Consider an electron in an infinite potential well of size 1 nm (a) What is...
6. Consider an electron in an infinite potential well of size 1 nm (a) What is the ground state (lowest energy level) energy of the electron? (b) What is the energy required to move an electron from ground state to the third energy level (n-3)? (c) What wavelength of photon would be emitted if the electron move from n-3 to its ground level? (Electron mass - 9.11 x 103 kg, h-1.055 x 1034 J.s, h 6.626 x 1034 J.s)
Exercise 5 Consider a particle in an infinite square well of length a. The particle is...
Exercise 5 Consider a particle in an infinite square well of length a. The particle is initially in the ground-state. The width of the potential well is suddenly changed by moving the right wall of the well from a to 2a. What is the probability of observing the particle in the ground-state of the new expanded well ?
4) A particle in an infinite square well 0 for 0
4) A particle in an infinite square well 0 for 0
A particle is in the ground state of a symmetric infinite square well with Vx) O for -a/2<x<+a/2, and infinite elsewhere. (a) The well then undergoes an instantaneous symmetric expansion to -a <<< ta. Calculate the probabilities of the particle being found in each of the three lowest energy states of the larger well. (b) Instead, suppose that the well expansion takes place adiabatically. Again, calculate the probabilities of the particle being found in each of the three lowest energy...
4) (2096) For an electron in a one-dimensional infinite square well of width L, find (a) (5%) < x >, (b) (5%) < x2 >, and (c) (5%) Δ). (d) (5%) What is the probability of finding the electron between x = 0.2 L and x = 0.4 L if the electron is in n=5 state
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny, and n, are integers. The corresponding allowed energies are Now let us introduce the perturbation otherwise a) Find the first-order correction to the ground state energy b) Find the first-order correction to the first excited state
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny,...
6. Show that for an infinite square well (p2-CanE), and compute (p2〉 for the ground state.
6. Show that for an infinite square well (p2-CanE), and compute (p2〉 for the ground state.
6. (a) Consider the infinite square well again. Let the width of the well be a and the particle mass be m. Find an expression for the probability that a particle in the state, vi will be found in the region a/4 <x<3a/4. (b) Repeat part (a) for the nth eigenstate, yn, for arbitrary n. Show that the answer reduces to the classical value of 2 as n 00.
6. Consider an electron in an infinite potential well of size 1 nm (a) What is the ground state (lowest energy level) energy of the electron? (b) What is the energy required to move an electron from ground state to the third energy level (n-3)? (c) What wavelength of photon would be emitted if the electron move from n-3 to its ground level? (Electron mass - 9.11 x 103 kg, h-1.055 x 1034 J.s, h 6.626 x 1034 J.s)
Exercise 5 Consider a particle in an infinite square well of length a. The particle is initially in the ground-state. The width of the potential well is suddenly changed by moving the right wall of the well from a to 2a. What is the probability of observing the particle in the ground-state of the new expanded well ?
4) A particle in an infinite square well 0 for 0
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