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64 Consider a particle in a one-dimensional box in the ground state v, and the first...
Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is...
Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by Knowing that the ground state of the particle at a certain instant is described by the wave function mw 1/4 _mw2 Th / calculate (for the ground state): a) The mean value of the position <x> (2 marks) b) The mean value of the position squared < x2 > (2 marks) c) the mean value of the momentum <p> (2...
7. What is the probability of finding a particle translating in the central third of a 1 dimensional box if it is in the (a) the ground state (b) the first excited state. (c) Compare these probab...
7. What is the probability of finding a particle translating in the central third of a 1 dimensional box if it is in the (a) the ground state (b) the first excited state. (c) Compare these probabiliies to the classical probability. (d) What is the average value for the position in the ground state? Do your answers make sense? 15P
7. What is the probability of finding a particle translating in the central third of a 1 dimensional box if...
Exercise 10.14 A particle is initially in its ground state in an infinite one-dimensional potential box...
Exercise 10.14 A particle is initially in its ground state in an infinite one-dimensional potential box with sides at x = 0 and x a. If the wall of the box at x-a is suddenly moved to x = 10a, calculate the probability of finding the particle in (a) the fourth excited (n = 5) state of the new box and (b) the ninth (n 10) excited state of the new box.
An electron is confined in the ground state in a one-dimensional box of width 10-10 m....
An electron is confined in the ground state in a one-dimensional box of width 10-10 m. Its energy is known to be 38 eV. (a) Calculate the energy of the electron in its first and second excited states (b) Sketch the wave functions for the ground state, the first and the second excited states (c) Estimate the average force (in Newtons) exerted on the walls of the box when the electron is in the ground state. (d) Sketch the new...
6. For a particle in a one-dimensional box, the ground state wave function is sin What...
6. For a particle in a one-dimensional box, the ground state wave function is sin What is the probability that the particle is in the right-hand half of the box? Ans: V/, or 50% а. b What is the probability that the partic le is in the middle third of the box? Ans: 0.609 or 60.9%
A particle of charge q and mass m is bound in the ground state of a one-dimensional harmonic osci...
A particle of charge q and mass m is bound in the ground state of a one-dimensional harmonic oscillator potential with frequency oo. At time t-0 a weak spatially uniform electric field (E) is turned on, so that the perturbation to the Hamiltonian can be described as R'(t) =-q Exe-t/t for t> 0. Using first order, time-dependent perturbation theory, calculate the following probabilities: (a) the particle is detected in the first excited state after a very long time (t »...
for a one dimensional particle in a box, write an integral expression for the average value,...
for a one dimensional particle in a box, write an integral expression for the average value, or expectation value, of the momentum of the n=1 state
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
Al hamonic poteantial with cigcnstat) definedb Consider a particle in a one-dimensional harmonic ...
al hamonic poteantial with cigcnstat) definedb Consider a particle in a one-dimensional harmonic potential with eigenstates |n〉 defined by A n)-E n . If the particle is initially in an equal superposition ofits groundstate and first excited state: |ψ(t-0 2. excited state: Ive-o)- )-11) (a) According to the time-dependent Schrodinger equation, what is the wavefunetion of the particle at a later time t (b) Find the expectation value of position as a function of time for the particle. Hint: use...
A particle of mass m is moving So, - Sasa V (2) elsewhere. a Find the...
A particle of mass m is moving So, - Sasa V (2) elsewhere. a Find the ground state, the first and second excited state wave functions. b Find expression for E1, E2 and E3. c Find the probability densities P2(x, t) and P3(x,t). d Calculate the expectation values (x)2, (x)3, (p)2 and (P)3. e Calculate the expectation values (22), (p)
Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by Knowing that the ground state of the particle at a certain instant is described by the wave function mw 1/4 _mw2 Th / calculate (for the ground state): a) The mean value of the position <x> (2 marks) b) The mean value of the position squared < x2 > (2 marks) c) the mean value of the momentum <p> (2...
7. What is the probability of finding a particle translating in the central third of a 1 dimensional box if it is in the (a) the ground state (b) the first excited state. (c) Compare these probabiliies to the classical probability. (d) What is the average value for the position in the ground state? Do your answers make sense? 15P
7. What is the probability of finding a particle translating in the central third of a 1 dimensional box if...
Exercise 10.14 A particle is initially in its ground state in an infinite one-dimensional potential box with sides at x = 0 and x a. If the wall of the box at x-a is suddenly moved to x = 10a, calculate the probability of finding the particle in (a) the fourth excited (n = 5) state of the new box and (b) the ninth (n 10) excited state of the new box.
An electron is confined in the ground state in a one-dimensional box of width 10-10 m. Its energy is known to be 38 eV. (a) Calculate the energy of the electron in its first and second excited states (b) Sketch the wave functions for the ground state, the first and the second excited states (c) Estimate the average force (in Newtons) exerted on the walls of the box when the electron is in the ground state. (d) Sketch the new...
6. For a particle in a one-dimensional box, the ground state wave function is sin What is the probability that the particle is in the right-hand half of the box? Ans: V/, or 50% а. b What is the probability that the partic le is in the middle third of the box? Ans: 0.609 or 60.9%
A particle of charge q and mass m is bound in the ground state of a one-dimensional harmonic oscillator potential with frequency oo. At time t-0 a weak spatially uniform electric field (E) is turned on, so that the perturbation to the Hamiltonian can be described as R'(t) =-q Exe-t/t for t> 0. Using first order, time-dependent perturbation theory, calculate the following probabilities: (a) the particle is detected in the first excited state after a very long time (t »...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
al hamonic poteantial with cigcnstat) definedb Consider a particle in a one-dimensional harmonic potential with eigenstates |n〉 defined by A n)-E n . If the particle is initially in an equal superposition ofits groundstate and first excited state: |ψ(t-0 2. excited state: Ive-o)- )-11) (a) According to the time-dependent Schrodinger equation, what is the wavefunetion of the particle at a later time t (b) Find the expectation value of position as a function of time for the particle. Hint: use...
A particle of mass m is moving So, - Sasa V (2) elsewhere. a Find the ground state, the first and second excited state wave functions. b Find expression for E1, E2 and E3. c Find the probability densities P2(x, t) and P3(x,t). d Calculate the expectation values (x)2, (x)3, (p)2 and (P)3. e Calculate the expectation values (22), (p)
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