Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 6, Problem 39E
To determine
The width of the separation between the two barriers.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A ID harmonic oscillator of angular frequency w and charge q is in its ground state at
time t=0. A perturbation H'(t) = qE eA3 (where E is ekctric field and ß is a constant) is
%3D
applied for a time t = t. Cakulate the probability of transition to the first and second
excited state. (hint: you may expand exponential in perturbation and keep it only up to
linear term)
Legrende polynomials
The amplitude of a stray wave is defined by:
SO) =x
(21+ 1) exp li8,] sen 8, P(cos 8).
INO
Here e is the scattering angle, / is the angular momentum and 6, is the phase shift produced by the
central potential that performs the scattering. The total cross section is:
Show that:
'É4+ 1)sen² 8, .
Suppose 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/#)²
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
- One-dimensional harmonic oscillators in equilibrium with a heat bath (a) Calculate the specific heat of the one-dimensional harmonic oscillator as a function of temperature. (b) Plot the T -dependence of the mean energy per particle E/N and the specific heat c. Show that E/N → kT at high temperatures for which kT > hw. This result corresponds to the classical limit and is shown to be an example of the equipartition theorem. In this limit the energy kT is large in comparison to ħw, the separation between energy levels. Hint: expand the exponential function 1 ē = ħw + eBhw (c) Show that at low temperatures for which ħw> kT , E/N = hw(+e-Bhw) What is the value of the heat capacity? Why is the latter so much smaller than it is in the high temperature limit? Why is this behavior different from that of a two-state system? (d) Verify that S →0 as T> O in agreement with the third law of thermodynamics, and that at high T,S> kN In(kT / hw).arrow_forwardA neutron of mass m of energy E a, V(x) = V, ) II. Calculate the total probability of neutron tunneling through the barrier?; from region I to II.arrow_forwardSuppose you measure A with eigenvalues A1, A2, and A3 with corresponding eigenvectors |1), 2), and |3), respectively, on wave function ) = a|1) + B|2) + y|3). Assuming degeneracy where A3, what normalized wave function does ) collapse to when normalized measuring A brings a value of 1? O a[1) + y|3) a² +y? a²+y? O alı)+r|3) Va2+y2arrow_forward
- Suppose a harmonic oscillator is subject to a perturbation av = Ahw (&/#0)* . where ro = mw/h is the length scale of the problem. a) Use Rayleigh-Schrödinger perturbation theory to find the first and second order corrections to the energies of the n'th level. b) Discuss the applicability of the perturbative approach for states with large n,arrow_forwardQ-Obtain expression of transition coefficient for a two level system up to first order, in the framework of time dependent perturbation theory. From this how the transition probability and transition rate can be calculated?arrow_forwardWhat would happen to the incident wave Þ(x) = Aelk* at x < 0 that sees a step potential in the form V(x) = iT in the positive x region? Here i is complex number and I is positive real number. (a) Explain in detail (perform some calculations too). (b) Calculate the reflection and transmission coefficients.arrow_forward
- Problem 3 For = [-1,2] and X(@) = w? - 1, find expressions for Fx(x) and fx(x) assuming that probability measure on 2 is the Lebesgue measure scaled by 1/3.arrow_forwardConsider a system of two Einstein solids, A and B, each containing10 oscillators, sharing a total of 20 units of energy. Assume that the solids areweakly coupled, and that the total energy is fixed. What is the probability of finding exactly half of the energy in solid A?arrow_forwardWhen 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} 2arrow_forward
- In the canonical ensemble, we control the variables T, p, and N, and the fundamental function is the Gibbs free energy (G). But if we control T, p, and μ, then we will have a different fundamental function, Z (This is the case for cells that often regulate their temperature, pressure, and chemical potentials to maintain equilibrium). Which of the below options should the Z function equal? H - TS - μN H + TS + μN H + TS - μN G + μN F - pV - μN -H + TS + μNarrow_forwardQualitatively, how would you expect the probability for a particle to tunnel through a potential barrier to depend on the height of the barrier? Explainarrow_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_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
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning