Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 6, Problem 37E
To determine
To verify:
The final tunnelling probability is
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
We have a free particle in one dimension at a time t = 0, the initial wave function is
(x, 0) = Ae-r|æ|
where A and r are positive real constants.
Calculate the expectation value (p).
When a particle of energy E approaches a potential barrier of height V0, where E >> V0, show that the refl ection coeffcient is about {[V0 sin(kL)]/2E} 2
Consider the following operators on a Hilbert space V³(C) :
0-i 0
SHABSB
101 Ly=
0 -i Lz 00 0
√2
0 i 0
LI
√2
010
010
10
00
0
If the particle is in state |L₂ = −1) and L₂ is measured, what are the possible outcomes and
their probabilities?
Chapter 6 Solutions
Modern Physics
Ch. 6 - Prob. 1CQCh. 6 - Prob. 2CQCh. 6 - Prob. 3CQCh. 6 - Prob. 4CQCh. 6 - Prob. 5CQCh. 6 - Prob. 6CQCh. 6 - Prob. 7CQCh. 6 - Prob. 8CQCh. 6 - Prob. 9CQCh. 6 - Prob. 10CQ
Ch. 6 - The diagram below plots (k) versus wave number for...Ch. 6 - Prob. 12CQCh. 6 - Prob. 13ECh. 6 - Prob. 14ECh. 6 - Prob. 15ECh. 6 - Prob. 16ECh. 6 - Prob. 17ECh. 6 - Prob. 18ECh. 6 - Prob. 19ECh. 6 - Prob. 20ECh. 6 - Prob. 21ECh. 6 - Prob. 22ECh. 6 - Prob. 23ECh. 6 - Prob. 24ECh. 6 - Prob. 25ECh. 6 - Prob. 26ECh. 6 - Prob. 27ECh. 6 - Prob. 28ECh. 6 - Obtain the smoothness conditions at the...Ch. 6 - Prob. 30ECh. 6 - Prob. 31ECh. 6 - Jump to Jupiter The gravitational potential energy...Ch. 6 - Prob. 33ECh. 6 - Obtain equation (618) from (616) and (617).Ch. 6 - Prob. 35ECh. 6 - Prob. 36ECh. 6 - Prob. 37ECh. 6 - Prob. 38ECh. 6 - Prob. 39ECh. 6 - Prob. 40ECh. 6 - Prob. 41ECh. 6 - Prob. 42ECh. 6 - Prob. 43ECh. 6 - Prob. 44ECh. 6 - Prob. 45ECh. 6 - Prob. 46ECh. 6 - Prob. 47ECh. 6 - Prob. 48ECh. 6 - Prob. 49ECh. 6 - Prob. 50ECh. 6 - Prob. 51CECh. 6 - Prob. 52CECh. 6 - Prob. 53CECh. 6 - Prob. 54CECh. 6 - Prob. 56CE
Knowledge Booster
Similar questions
- Denoting by ,m) the eigenvectors of L² and L₂, consider the vector 3 √51¹, -1) + √(1,0) +1,1) (26) = (a) If L₂ is measured, what values can be obtained, and with which probability? (b) Calculate the expectation value of L.arrow_forwardIn a simple model for a radioactive nucleus, an alpha particle (m = 6.64 * 10-27 kg) is trapped by a square barrier that has width 2.0 fm and height 30.0 MeV. (a) What is the tunneling probability when the alpha particle encounters the barrier if its kinetic energy is 1.0 MeV below the top of the barrier (Fig. )? (b) What is the tunneling probability if the energy of the alpha particle is 10.0 MeV below the top of the barrier?arrow_forwardA simple model of a radioactive nuclear decay assumes that a-particles are trapped inside a well of nuclear potential that walls are the barriers of a finite width 2.0 fm and height 30.0 MeV. Find the tunneling probability across the potential barrier of the wall for a-particles having kinetic energy (a) 29.0 MeV and (b) 20.0 MeV. The mass of the a -particle is m=6.641027kg.arrow_forward
- Compute |(x,t)|2 for the function (x,t)=(x)sint, where is a real constant.arrow_forwardA particle of mass m is confined to a box of width L. If the particle is in the first excited state, what are the probabilities of finding the particle in a region of width0.020 L around the given point x: (a) x=0.25L; (b) x=040L; (c) 0.75L and (d) x=0.90L.arrow_forwardA particle with mass 2.5 × 10^(-27) kg and energy 4.0 eV approaches a potential barrier with a height of 2.5 eV and a width of 1.0 nm. Calculate the probability of the particle tunneling through the barrier.arrow_forward
- p , For a step potential function at x = 0, the probability that a particle exists in the region x > 0 is (A) zero. (B) 1. (C) larger than zero. (D) larger than 1.arrow_forwardConsider the wavefunction for a particle in a one-dimensional box when the level is n = 6. Calculate the total probability of finding the particle between x = 0 and x = L/12? Provide your answer to three significant figures.arrow_forwardConsider an electron of energy 1 eV that encounters a potential barrier of width 0.1nm and energy height 2ev. what is the probability of the electron crossing the barrier? repeat the same calculation for a protonarrow_forward
- Consider a particle with the following wave-function: ,xL and L and A are constants. (a) What is the normalization constant A (in terms of L)? (b) What is (in terms of L)? ? (ie, ) (c) What is the probability that the particle will be found within x=0 and L/2?arrow_forwardA quantum mechanical particle is confined to a one-dimensional infinite potential well described by the function V(x) = 0 in the region 0 < x < L, V(x) = ∞ elsewhere. The normalised eigenfunctions for a particle moving in this potential are: Yn(x) = √ 2 Nπ sin -X L L where n = 1, 2, 3, .. a) Write down the expression for the corresponding probability density function. Sketch the shape of this function for a particle in the ground state (n = 1). b) Annotate your sketch to show the probability density function for a classical particle moving at constant speed in the well. Give a short justification for the shape of your sketch. c) Briefly describe, with the aid of a sketch or otherwise, the way in which the quantum and the classical probability density functions are consistent with the correspondence principle for large values of n.arrow_forwardSuppose the perturbation has time dependence: H = Veut, for the initial conditions: Ca (0) = 1. 2 Ch(0) = 0 %3! The transition probability is .a sin (w t), where w =(w -w (t): ab 2rw ab .b Pa-olt) =| 2ho, cos (m,t), where w, =/ (@-w)² +(V»/)° .C Pamol) = sin (0,t), where w, = (@-w,)² +(V»/+)° .d Pa-b(t) = , where w, =(w-j²+(Væ/#)²arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning