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5 Suppose that a particle in a 1-dimensional box is in the state (x) = NxL-x)...
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...
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimens...
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimension x is given by the following expression: x <0,x>2L (A) Determine the value of the normalization constant c. (B) Draw the wavefunction. (C) Calculate Prob(L/2 S x 3 3L/2), the probability of finding the particle between x - L/2 and 3L/2
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimension x is given by the following expression:...
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (...
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: 12 21 Where L is the total angular momentum operator,...
1. For the one-dimensional particle in a box of length L=1A a. Write an integral expression for the probability of findi...
1. For the one-dimensional particle in a box of length L=1A a. Write an integral expression for the probability of finding the particle between L/4 and L/3, for the fourth excited state. b. Write the wavefunction for the fourth excited state c. Calculate the numerical probability of finding the particle between 0 and L/3, for the ground state. I am having trouble understanding these questions for my practice assignment, I have an exam tonight and I want to be able...
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 with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to e...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
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...
please solve with explanations 3. (20 pts) A particle of mass m and charge q is in a one dimensional harmonic oscillato...
please solve with explanations
3. (20 pts) A particle of mass m and charge q is in a one dimensional harmonic oscillator potential ()1ma'. A time dependent uniform electric field E, ()E, os eris 2 applied in the x direction. The particle is in the harmonic oscillator ground state at time a) What is the time dependent perturbation Hamiltonian H'(t) - the potential enegy of the charge in this electric field? b) Find the amplitude ci(t) of finding the particle...
help Part B. Open questions. 1. (30 points) For the one-dimensional particle in a box of...
help
Part B. Open questions. 1. (30 points) For the one-dimensional particle in a box of length L. a. Write the wavefunction for the fifth excited state b. Calculate the energy for the fifth excited state when L = 18 and m = Ing. c. Write an integral expression for the probability of finding the particle between L/4 and L/2, for the second excited state. d. Calculate the numerical probability of finding the particle between 0 and L15, for the...
Consider a particle with mass m described by the Hamilton operator for a one-dimensional harmonic oscillator...
Consider a particle with mass m described by the Hamilton operator for a one-dimensional harmonic oscillator 2 Zm 2 The normalized eigenfunctions for Hare φη (x) with energies E,,-(n + 2) ha. At time t-0 the wavefunction of the particle is given by у(x,0)- (V3іфі (x) + ф3(x)). Now let H' be an operator given by where k is a positive constant. 1) Show that H' is Hermitian. 2) Express H' by the step-operators a+ and a 3) Calculate the...
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...
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimension x is given by the following expression: x <0,x>2L (A) Determine the value of the normalization constant c. (B) Draw the wavefunction. (C) Calculate Prob(L/2 S x 3 3L/2), the probability of finding the particle between x - L/2 and 3L/2
Probability. A wavefunction ψ(x) describing the state of a particle free to move along one dimension x is given by the following expression:...
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: 12 21 Where L is the total angular momentum operator,...
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 with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
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...
please solve with explanations
3. (20 pts) A particle of mass m and charge q is in a one dimensional harmonic oscillator potential ()1ma'. A time dependent uniform electric field E, ()E, os eris 2 applied in the x direction. The particle is in the harmonic oscillator ground state at time a) What is the time dependent perturbation Hamiltonian H'(t) - the potential enegy of the charge in this electric field? b) Find the amplitude ci(t) of finding the particle...
help
Part B. Open questions. 1. (30 points) For the one-dimensional particle in a box of length L. a. Write the wavefunction for the fifth excited state b. Calculate the energy for the fifth excited state when L = 18 and m = Ing. c. Write an integral expression for the probability of finding the particle between L/4 and L/2, for the second excited state. d. Calculate the numerical probability of finding the particle between 0 and L15, for the...
Consider a particle with mass m described by the Hamilton operator for a one-dimensional harmonic oscillator 2 Zm 2 The normalized eigenfunctions for Hare φη (x) with energies E,,-(n + 2) ha. At time t-0 the wavefunction of the particle is given by у(x,0)- (V3іфі (x) + ф3(x)). Now let H' be an operator given by where k is a positive constant. 1) Show that H' is Hermitian. 2) Express H' by the step-operators a+ and a 3) Calculate the...
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