Question

The ground state of a particle is given by the time‐dependent wave function Ψ0(x, t) =...

The ground state of a particle is given by the time‐dependent wave function
Ψ0(x, t) = Aeαx^2+iβt​​​​​​
with an energy eigenvalue of E0 = ħ2α/m
a. Determine the potential in which this particle exists. Does this potential resemble any that you have seen before?
b. Determine the normalization constant A for this wave function.
c. Determine the expectation values of x, x2, p, and p2.
d. Check the uncertainty principle Δx and Δp. Is their product consistent with the uncertainty principle?

Science   Advanced-Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1


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
Consider the time-dependent ground state wave function Ψ(x,t ) for a quantum particle confined to an...
Consider the time-dependent ground state wave function Ψ(x,t ) for a quantum particle confined to an impenetrable box. (a) Show that the real and imaginary parts of Ψ(x,t) , separately, can be written as the sum of two travelling waves. (b) Show that the decompositions in part (a) are consistent with your understanding of the classical behavior of a particle in an impenetrable box.
1, Show that the real and imaginary parts (separately) of the time-dependent ground state wave function...
1, Show that the real and imaginary parts (separately) of the time-dependent ground state wave function psi(x,t) for a particle confined to an impenetrable box can be written as a linear combination of two traveling waves. 2, Show the decomposition in (1) is consistent with the classical behavior of a particle in an impenetrable box.
7. A particle of mass m is described by the wave function ψ ( x) =...
7. A particle of mass m is described by the wave function ψ ( x) = 2a^(3/2)*xe^(−ax) when x ≥ 0 0 when x < 0 (a) (2 pts) Verify that the normalization constant is correct. (b) (3 pts) Sketch the wavefunction. Is it smooth at x = 0? (c) (2 pts) Find the particle’s most probable position. (d) (3 pts) What is the probability that the particle would be found in the region (0, 1/a)? 8. Refer to the...
Find the wave function for the ground state and first two excited states for a particle...
Find the wave function for the ground state and first two excited states for a particle in an infinitely deep square well of width a. Show that the uncertainty relation is satisfied for position and momentum.
Consider the following wave function: Psi(x,t) = Asin(2piBx)e^(-iCt) for 0<x<1/2B Psi(x,t) = 0 for all other...
Consider the following wave function: Psi(x,t) = Asin(2piBx)e^(-iCt) for 0<x<1/2B Psi(x,t) = 0 for all other x where A,B and C are some real, positive constants. a) Normalize Psi(x,t) b) Calculate the expectation values of the position operator and its square. Calculate the standard deviation of x. c) Calculate the expectation value of the momentum operator and its square. Calculate the standard deviation of p. d) Is what you found in b) and c) consistent with the uncertainty principle? Explain....
The wave function of a particle is ψ (x) = Ne (-∣x∣ / a) e (iP₀x...
The wave function of a particle is ψ (x) = Ne (-∣x∣ / a) e (iP₀x / ℏ). Where a and P0 are constant; (e≃2,71 will be taken). a) Find the normalization constant N? b) Calculate the probability that the particle is between [-a / 2, a / 2]? c) Find the mean momentum and the mean kinetic energy of the particle in the x direction.
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are positive real constants. (a) Using the normalization condition, find b in terms of a. (b) What is the probability to find the particle at x = 0.33a in a small interval of width 0.01a? (c) What is the probability for the particle to be found...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are positive real constants. (a) Using the normalization condition, find b in terms of a. (b) What is the probability to find the particle at x = 0.33a in a small interval of width 0.01a? (c) What is the probability for the particle to be found...
Consider the ground state of the harmonic oscillator. (a) (7 pts) Calculate the expectation values <x>,...
Consider the ground state of the harmonic oscillator. (a) (7 pts) Calculate the expectation values <x>, <x2>, <p> and <p2>. (b) (3 ps) What is the product ΔxΔp, where the two quantities are standard deviations? (This is easy if you did part (a)). How does this answer compare with the prediction of the Uncertainty Principle?
For the wave function ψ(x) defined by ψ(x)= A(a-x),x<a ψ(x)=0, x>=a (a) Sketch ψ(x) and calculate...
For the wave function ψ(x) defined by ψ(x)= A(a-x),x<a ψ(x)=0, x>=a (a) Sketch ψ(x) and calculate the normalization constant A. ( b) Using Zettili’s conventions, find its Fourier transform φ(k) and sketch it. (c) Using the ψ(x) and φ(k), make reasonable estimates for ∆x and ∆k. Using p = ħk, check whether your results are compatible with the uncertainty principle.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT