Question

Consider two rigid walls at x=0 and x=L. There is a partition at x=L/2 and the...

Consider two rigid walls at x=0 and x=L. There is a partition at x=L/2 and the particle is in the ground state on the left side of the partition, that is between x=0 and x=L/2. At t=0, the partition is removed. Determine y(x,t) for t ≥ 0
Science   Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

At t = 0 the wave function is

for 0 < x <L/2

and it is zero

for L/2 < x < L

At a finite time the wave function is in a linear combination of wave function for a particle in a box of length L

Therefore at = 0

Therfore

Substituting for t = 0 value from the first equaiton gives

or

which is zero for even values of n

Therefore

where

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The sides of a one dimensional quantum box (1-D) are in x=0, x=L. The probability of...
The sides of a one dimensional quantum box (1-D) are in x=0, x=L. The probability of observing a particle of mass m in the ground state, in the first excited state and in the 2nd excited state are 0.6, 0.3, and 0.1 respectively a) If each term contributing to the particle function has a phase factor equal 1 in t=0. What is the wave function for t>0? b) what is the probability of finding the particle at the position x=L/3...
Consider a wave packet of a particle described by the wavefunction ψ(x,0) = Axe^−(x^2/L^2), -∞ ≤  x...
Consider a wave packet of a particle described by the wavefunction ψ(x,0) = Axe^−(x^2/L^2), -∞ ≤  x ≤ ∞. a) Draw this wavefunction, labeling the axes in terms of A and L. b) Find the relationship between A and L that satisfies the normalization condition. c) Calculate the approximate probability of finding the particle between positions x = −L and x = L. d) What are 〈x〉, 〈x^2〉, and σ_x ? (Hint: use shortcuts where possible). e) Find the minimum uncertainty...
2. A cylindrical vessel with rigid adiabatic walls is separated into two parts by a frictionless...
2. A cylindrical vessel with rigid adiabatic walls is separated into two parts by a frictionless adiabatic piston. Each part contains 50.0 L of an ideal monatomic gas with Cv,m = 3R/2. Initially, Ti = 298 K, Pi = 1.0 bar in each part. Heat is slowly introduced into the left part using an electrical heater until the piston has moved sufficiently to the right to result in a final pressure Pf = 7.50 bar in the right part. Consider...
Exercise 3. Consider a particle with mass m in a two-dimensional infinite well of length L,...
Exercise 3. Consider a particle with mass m in a two-dimensional infinite well of length L, x, y ∈ [0, L]. There is a weak potential in the well given by V (x, y) = V0L2δ(x − x0)δ(y − y0) . Evaluate the first order correction to the energy of the ground state.    Evaluate the first order corrections to the energy of the first excited states for x0 =y0 = L/4. For the first excited states, find the points...
Exercise 40.48 from Young/Freedman, University Physics with Modern Physics, 14e Consider a particle in a box...
Exercise 40.48 from Young/Freedman, University Physics with Modern Physics, 14e Consider a particle in a box with rigid walls at x=0 and x=L. Let the particle be in the ground level. Part A Calculate the probability |ψ|2dx that the particle will be found in the interval x to x+dx for x=L/4. (Express your answer in terms of the variables dx and L.) Part B Calculate the probability |ψ|2dx that the particle will be found in the interval x to x+dx...
Consider a two-particle system. Each particle can have energy 0 and Δ. Compute the partition function...
Consider a two-particle system. Each particle can have energy 0 and Δ. Compute the partition function for the following case: a. When particles are distinguishable. b. When particles are fermions. c. When particles are Bosons.
Consider a container divided by a partition into two chambers. The first chamber contains 15kg of...
Consider a container divided by a partition into two chambers. The first chamber contains 15kg of water at 350°C, 1.2 MPa. The other chamber contains 19kg of water at 105°C with 60 percent of the mass is in the liquid phase. The partition is now removed and the water in both chambers are allowed to mix until the system reaches a thermal equilibrium of 120°C. Determine (a) the final pressure in the container (b) the vapor mass fraction at the...
Consider two random variables, X and Y, with joint PDF fxy(x,y)=e-2|y-x^2|-x    x>=0 , y can...
Consider two random variables, X and Y, with joint PDF fxy(x,y)=e-2|y-x^2|-x    x>=0 , y can be any value fxy(x,y)=0 otherwise (1) Determine fY|X(y|x) (2)Determine E[Y|X=x]
The normalized wave functions for the particle is in a 1D box of length L., with...
The normalized wave functions for the particle is in a 1D box of length L., with limits on x = 0 and x = L. V (x) = 0 for 0 <= x <= L and V (x) = Infinity elsewhere. The probability of a particle being between x = 0 and x = L / 8 in the ground quantum state (n = 1) should be calculated.
Recall that |ψ|2dx is the probability of finding the particle that has normalized wave function ψ(x)...
Recall that |ψ|2dx is the probability of finding the particle that has normalized wave function ψ(x) in the interval x to x+dx. Consider a particle in a box with rigid walls at x=0 and x=L. Let the particle be in the first excited level and use ψn(x)=2L−−√sinnπxL For which values of x, if any, in the range from 0 to L is the probability of finding the particle zero? For which v alues of x is the probability highest?Express your...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT