Question

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.

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

Homework Answers

Answer #2

answered by: anonymous
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
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.
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...
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...
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.
Intro to Quantum Mechanics (Free particle) a). Write the relations between the wave vector and angular...
Intro to Quantum Mechanics (Free particle) a). Write the relations between the wave vector and angular frequency of a free particle and its momentum vector and energy. b) What is the general form in one dimension of the wave function for a free particle of mass m and momentum p? c) Can this wave function ever be entirely real? If so, show how this is possible. If not, explain why not. d) What can you say about the integral of...
4 Schr¨odinger Equation and Classical Wave Equation Show that the wave function Ψ(x, t) = Ae^(i(kx−ωt))...
4 Schr¨odinger Equation and Classical Wave Equation Show that the wave function Ψ(x, t) = Ae^(i(kx−ωt)) satisfies both the time-dependent Schr¨odinger equation and the classical wave equation. One of these cases corresponds to massive particles, such as an electron, and one corresponds to massless particles, such as a photon. Which is which? How do you know?
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...
A free particle has the initial wave function Ψ(x, 0) = Ae−ax2 where A and a...
A free particle has the initial wave function Ψ(x, 0) = Ae−ax2 where A and a are real and positive constants. (a) Normalize it. (b) Find Ψ(x, t). (c) Find |Ψ(x, t)| 2 . Express your result in terms of the quantity w ≡ p a/ [1 + (2~at/m) 2 ]. At t = 0 plot |Ψ| 2 . Now plot |Ψ| 2 for some very large t. Qualitatively, what happens to |Ψ| 2 , as time goes on? (d)...
The wave function for a particle confined to a one-dimensional box located between x = 0...
The wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by Psi(x) = A sin (n(pi)x/L) + B cos (n(pi)x/L) . The constants A and B are determined to be
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT