Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 36AP
To determine
The order of magnitude of the probability of escaping through the wall.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Photos - B4.jpg
A See all photos
+ Add to
* Edit & Create v
IA Share
A particle of mass, m, moves freely inside an infinite potential well spanning the range, 0
For a particle in a box, what would the probability distribution function Ic I2 look like if the particle behaved like a classical (Newtonian) particle? Do the actual probability distributions approach this classical form when n is very large? Explain.
Physics Department
PHYS4101 (Quantum Mechanics)
Assignment 2 (Fall 2020)
Name & ID#.
A three-dimensional harmonic oscillator of mass m has the potential energy
1
1
1
V(x.y.2) = ; mw*x² +mwży² +=mw;z?
where w1 = 2w
a. Write its general eigenvalues and eigenfunctions
b. Determine the eigenvalues and their degeneracies up to the 4th excited state
c. The oscillator is initially equally likely found in the ground, first and second excited states and
is also equally likely found among the states of the degenerate levels. Calculate the expectation
values of the product xyz at time t
Chapter 40 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.5 - Prob. 40.4QQCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6P
Ch. 40 - Prob. 7PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 13PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Two particles with masses m1 and m2 are joined by...Ch. 40 - Prob. 31APCh. 40 - Prob. 32APCh. 40 - Prob. 33APCh. 40 - Prob. 34APCh. 40 - Prob. 36APCh. 40 - Prob. 37APCh. 40 - Prob. 38APCh. 40 - Prob. 39APCh. 40 - Prob. 40APCh. 40 - Prob. 41APCh. 40 - Prob. 42APCh. 40 - Prob. 44CPCh. 40 - Prob. 46CPCh. 40 - Prob. 47CP
Knowledge Booster
Similar questions
- A marble rolls back and forth across a shoebox at a constant speed of 0.8 m/s. Make an order-of-magnitude estimate of the probability of it escaping through the wall of the box by quantum tunneling. State the quantities you take as data and the values you measure or estimate for them.arrow_forwardWhich of the following statements related to quantum statistics are true? Select one or more: a.The wave function of a pair of bosons is symmetric with respect to the exchange of particles. b.If the particle density of an ideal gas is very low (that is, the particle density is much less than the cube of the thermal de Broglie wavelength), quantum effects are important. c.In the case of a rare gas and at high enough temperatures, the Fermi-Dirac and Bose-Einstein distributions are approximately the same. d.Two bosons cannot be in the same quantum state.arrow_forwardThe creation of elements in the early universe and in stars involves protons tunneling through nuclei. Find the probability of the proton tunneling through 12C when the temperature of the star containing the proton and carbon is 12,000 Karrow_forward
- A particle in the ground state of the quantum harmonic oscillator has a wavefunction that can be written as found in image where a = mω/hbar , and where N, m and ω are all constants. For this particle: a) Find an expression for the normalization constant N, in terms of a. b) Derive an expression for the uncertainty in the momentum, ∆p. N.B. You may wish to refer to the Appendix when answering this question.arrow_forward6. A set of N classical oscillators in one dimension is given by the Hamil- tonian N Σ (2²m² ² + 1/ mw³²q² ) . i=1 H=Σ Using the formalism of the canonical ensemble in classical phase space, obtain expressions for the partition function, the energy per oscillator, the entropy per oscillator, and the specific heat. Compare with the results from the classical limit of the quantum oscillator. Calculate an expression for the quadratic deviation of the energy as a function of temperature.arrow_forwardA particle with an energy of 20.0 eV is initially travelling in a region in which the potential energy is zero. The particle is incident upon a potential energy barrier which has a height of 14.0 eV. Treat this problem quantum mechanically.What is the probability that the particle will be reflected by the barrier?What is the probability that the particle will be transmitted past the barrier?arrow_forward
- A quantum system has a ground state with energy Eo = 0 meV and a 2-fold degenerate excited state with energy E₁ = 50 meV. E1 Calculate the probability of finding the system in its ground state when it is at T = 300 K. Select one: O a. 0.78 O b. 0.22 O c. 1 O d. 0.87arrow_forwardAn electron approaches a 1.0-nm-wide potential-energy barrier of height 6.1 eV. You may want to review (Pages 1169 - 1172) Part A What energy electron has a tunneling probability of 10%? Express your answer to three significant figures and include the appropriate units. HÁ E = Value Units Submit Request Answer Part B What energy electron has a tunneling probability of 1.0%? Express your answer to three significant figures and ncluc appropriate units. ? E = Value Units Submit Request Answer Part C What energy electron has a tunneling probability of 0.10%? Express your answer to three significant figures and include the appropriate units. HA E = Value Units Submit Request Answerarrow_forwardSuppose Fuzzy, a quantum-mechanical duck, lives in a world in which h = 2 J s. Fuzzy has a mass of 1.90 kg and is initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in the duck's speed? m/s (b) Assuming this uncertainty in speed to prevail for 4.90 s, determine the uncertainty in Fuzzy's position after this time. marrow_forward
- No Spacing Heading 1 Normal Aa v A A 困、 Paragraph Styles The action along a path is defined to be: S = [(K.E.-P. E.) dt Determine the physical units of action. Detail Feynman's approach to calculating the probability amplitude for an electron to go from one event A to another B using the "sum over all paths". A'Focus 12 1> 12arrow_forwardFor statistical problems in general: on a flat and level square the drunkard moves 3 steps and the distance for each step is 20 cm. A. Find the probability that he is 20 cm to the right of the lamp. B. All possible steps and a probability diagram is drawn.arrow_forwardCalculate the probability that a particle in a one- dimensional box of length a is found between 0.32a and 0.35a when it is described by the following wave functions: a. b. π.Χ. sin a √ sin (³7.x) a What would you expect for a classical particle? Compare your results for (a) and (b) with the classical result.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning