Question

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 previous problem. (a) (2 pts) Find the expectation value for the position in terms of a. (b) (4 pts) The particle has energy E = 0. Show using the Schrodinger equation that the potential energy function is U ( x) = (− ahbar^2/ mx) + (a ^2 * hbar^2 )/2m

(c) (4 pts) Find the probability that the particle is in the forbidden region (E < U)

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
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...
The state of a particle is completely described by its wave function Ψ(?,?) One-dimensional Schrodinger Equation--...
The state of a particle is completely described by its wave function Ψ(?,?) One-dimensional Schrodinger Equation-- answer the following questions: 2) Show that when U(x) = 0, and , is a solution to the one-?=2??/ℏΨ=?sin??dimensional Schrodinger equation. 3) Show that when U(x) = 0, and , is a solution to the one-?=2??/ℏΨ=?cos??dimensional Schrodinger equation. 4) Show that where A and B are constants is a solution to the Ψ=??+?Schrodinger equation when U(x) = 0, and when E = 0.
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.
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...
A particular positron is restricted to one dimension and has a wave function given by ψ(x)=...
A particular positron is restricted to one dimension and has a wave function given by ψ(x)= Ax between x = 0 and x = 1.00 nm, and ψ(x) = 0 elsewhere. Assume the normalization constant A is a positive, real constant. (a) What is the value of A (in nm−3/2)? nm−3/2 (b) What is the probability that the particle will be found between x = 0.290 nm and x = 0.415 nm? P = (c) What is the expectation value...
a. Suppose that at time ta the state function of a one particle system is Ψ...
a. Suppose that at time ta the state function of a one particle system is Ψ = (2/πc2)3/4 e(exp [– (x2 + y2 + z2)/c2)] where c = 2 nm. Find the probability that a measurement of the particle’s position at ta will find the particle in the tiny cubic region with its center at x = 1.2 nm, y = -1.0 nm, z = 0 and with edges each of length 0.004 nm. Note that 1 nm = 10-9...
The wave function of a particle in a one-dimensional box of length L is ψ(x) =...
The wave function of a particle in a one-dimensional box of length L is ψ(x) = A cos (πx/L). Find the probability function for ψ. Find P(0.1L < x < 0.3L) Suppose the length of the box was 0.6 nm and the particle was an electron. Find the uncertainty in the speed of the particle.
Consider the wave function at t = 0, ψ(x, 0) = C sin(3πx/2) cos(πx/2) on the...
Consider the wave function at t = 0, ψ(x, 0) = C sin(3πx/2) cos(πx/2) on the interval 0 ≤ x ≤ 1. (1) What is the normalization constant, C? (2) Express ψ(x,0) as a linear combination of the eigenstates of the infinite square well on the interval, 0 < x < 1. (You will only need two terms.) (3) The energies of the eigenstates are En = h̄2π2n2/(2m) for a = 1. What is ψ(x, t)? (4) Compute the expectation...
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