Homework Answers
Add Answer to:
3 Rockin' in the Free World Consider a free particle whose state at time t 0...
0 is given by a gaussian wave packet Consider a free particle whose state at time...
0 is given by a gaussian wave packet Consider a free particle whose state at time t (x, 0) Ae2/a2 for real constants A, a. (a) Normalize (r, 0), i.e., find A (b) Find (r, t). You can do the integral by completing the square in the exponent to get it into the form of a gaussian (c) Compute the probability density (, t), expressing your answer in terms of the quantity w av1(2ht/ma2)2 Sketch the probability density as a...
5. A free particle has the initial wave function, where A and a are positive real...
5. A free particle has the initial wave function, where A and a are positive real constants. (a) Normalize ψ(x,0). (b) Find φ(k). (c) Construct $(z,t), in the forn of an integral. (d) Discuss the limiting cases (a very large, and a very small).
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a...
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?
Problem 3: A free particle of mass m in one dimension is in the state Hbr...
Problem 3: A free particle of mass m in one dimension is in the state Hbr Ψ(z, t = 0) = Ae-ar with A, a and b real positive constants. a) Calculate A by normalizing v. b) Calculate the expectation values of position and momentum of the particle at t 0 c) Calculate the uncertainties ΔΧ and Δ1) for the position and momentum at t 0, Do they satisfy the Heisenberg relation? d) Find the wavefunction Ψ(x, t) at a...
3. Consider a free particle on a circle. That is, consider V(z) = 0 and wave...
3. Consider a free particle on a circle. That is, consider V(z) = 0 and wave functions Ψ(z, t) which are periodic functions of z: Ψ(z,t) = Ψ(z + L, t). a) Solve the Time-Independent Schroedinger equation. For each allowed energy, En, you will find two solutions, (s). Why does this not contradict the theorem that we proved in class about the non-degeneracy of the solutions to the TISE in one dimension? b) Start with the initial condition Ψ(z,0) sin2(nz/L)....
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0,...
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0, otherwise where a and A are positive real numbers. The particle is in a zero (or constant) potential environment since it is a free particle a) Determine A from normalization. b) Determine φ(p) = Φ(p,0), the time-zero momentum representation of the particle state. What is Φ(p,t)? Sketch φ(p). Locate the global maximum and the zeros of φ(p). Give the expression for the zeros (i.e.,...
Problem 2: Time development of a free particle The wave function of a free particle at time t- 0 is given by exp(2K1T N...
Problem 2: Time development of a free particle The wave function of a free particle at time t- 0 is given by exp(2K1T Now answer the questions below. l. what is the time evolved wave function ψ(z,t) ? points 2. What is the average momentum at any future time? 4 points 3. What is the average energy at any future time ? 3 points
Problem 2: Time development of a free particle The wave function of a free particle at...
(15 points) (Straightforward, but part (c) is probably longer) Consider a particle in the infinite square...
(15 points) (Straightforward, but part (c) is probably longer) Consider a particle in the infinite square well with the following wavefunction at t 0: V (x,0) 0, otherwise. n(x) is the nth solution to the time independent Schrodinger equation, as discussed in the where class. (a) Find the constant A that will normalize 1, at t-: 0, Will this constant normalize Ψ(x, t) for all time, t (b) Find Ψ(r,t). (c) At time, t-0 find (z), (p), Oz and Op....
A free particle moving in one dimension has wave function Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)] where k and ω are...
A free particle moving in one dimension has wave function Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)] where k and ω are positive real constants. At t = π/(6ω) what are the two smallest positive values of x for which the probability function |Ψ(x,t)|2 is a maximum? Express your answer in terms of k.
Studying through lecture slides for a quiz - can someone explain how we were supposed to...
Studying through lecture slides for a quiz - can someone explain
how we were supposed to know A=? And how we arrived at y= for the
integral?
Example: Gaussian wave packet A free particle has the initial wave function. Find Y(x,t). O how to knows Y(x,0) = Ae -ax? A=291942 Here a and A are real and positive. What is A? 1/4 V too A. a Bova c. a D. (29) 1/4 At = 0 $(x) = vzw Sa Pille-ikody...
0 is given by a gaussian wave packet Consider a free particle whose state at time t (x, 0) Ae2/a2 for real constants A, a. (a) Normalize (r, 0), i.e., find A (b) Find (r, t). You can do the integral by completing the square in the exponent to get it into the form of a gaussian (c) Compute the probability density (, t), expressing your answer in terms of the quantity w av1(2ht/ma2)2 Sketch the probability density as a...
5. A free particle has the initial wave function, where A and a are positive real constants. (a) Normalize ψ(x,0). (b) Find φ(k). (c) Construct $(z,t), in the forn of an integral. (d) Discuss the limiting cases (a very large, and a very small).
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?
Problem 3: A free particle of mass m in one dimension is in the state Hbr Ψ(z, t = 0) = Ae-ar with A, a and b real positive constants. a) Calculate A by normalizing v. b) Calculate the expectation values of position and momentum of the particle at t 0 c) Calculate the uncertainties ΔΧ and Δ1) for the position and momentum at t 0, Do they satisfy the Heisenberg relation? d) Find the wavefunction Ψ(x, t) at a...
3. Consider a free particle on a circle. That is, consider V(z) = 0 and wave functions Ψ(z, t) which are periodic functions of z: Ψ(z,t) = Ψ(z + L, t). a) Solve the Time-Independent Schroedinger equation. For each allowed energy, En, you will find two solutions, (s). Why does this not contradict the theorem that we proved in class about the non-degeneracy of the solutions to the TISE in one dimension? b) Start with the initial condition Ψ(z,0) sin2(nz/L)....
Problem 2: Time development of a free particle The wave function of a free particle at time t- 0 is given by exp(2K1T Now answer the questions below. l. what is the time evolved wave function ψ(z,t) ? points 2. What is the average momentum at any future time? 4 points 3. What is the average energy at any future time ? 3 points
Problem 2: Time development of a free particle The wave function of a free particle at...
(15 points) (Straightforward, but part (c) is probably longer) Consider a particle in the infinite square well with the following wavefunction at t 0: V (x,0) 0, otherwise. n(x) is the nth solution to the time independent Schrodinger equation, as discussed in the where class. (a) Find the constant A that will normalize 1, at t-: 0, Will this constant normalize Ψ(x, t) for all time, t (b) Find Ψ(r,t). (c) At time, t-0 find (z), (p), Oz and Op....
Studying through lecture slides for a quiz - can someone explain
how we were supposed to know A=? And how we arrived at y= for the
integral?
Example: Gaussian wave packet A free particle has the initial wave function. Find Y(x,t). O how to knows Y(x,0) = Ae -ax? A=291942 Here a and A are real and positive. What is A? 1/4 V too A. a Bova c. a D. (29) 1/4 At = 0 $(x) = vzw Sa Pille-ikody...
Most questions answered within 3 hours.
-
Humans have used horses for transportation for millions of
years. Therefore, they will use horses for...
asked 13 minutes ago -
The following are the Jensen Corporation's unit costs of making
and selling an item at a...
asked 48 minutes ago -
Does direct Medicare reimbursement of Advanced practice nurses
increase access to their services?
asked 1 hour ago -
List and explain why a company would choose to use a
published
compensation survey vs. creating...
asked 1 hour ago -
A discrete random variable X can take values from 1 to 10. Find
the variance of...
asked 1 hour ago -
The primary financial goal of a corporation is to maximize:
shareholders wealth.
earnings per share.
stock...
asked 2 hours ago -
determine whether the vectors u=(1,2,3,), v=(-2,1,0) and
w=(1,0,1) are linearly dependent or independent.
asked 2 hours ago -
python
Define a function called print_values which takes a dictionary
object as a parameter. The function...
asked 3 hours ago -
In Chapter 1 you created a program named Triangle in
which you displayed a seven-line triangle...
asked 3 hours ago -
Research question: What are the differences between separately
stated and non separately stated transactions in an...
asked 3 hours ago -
By using Arduino write a code that connects two LEDs to two
push-buttons. Each button controls...
asked 4 hours ago -
Bank of America has bonds that pay a coupon interest rate of 5.5
percent and mature...
asked 5 hours ago