Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 6, Problem 56CE
To determine
To show:
The energy quantization condition for the infinite well is
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(a) Find the s-wave phase shift, as a function of wave number k, for
spherically symmetric potential which is infinitely repulsive inside of a
1alius ro, and vanishes outside of ro.
(b) For k + 0 discuss the behavior of the phase shifts in the higher
pitrtial waves.
A particle of mass m is bound in a one-dimensional well with one impenetrable wall. The potential energy is given by the equation in the first provided image and the well is depticed in the second provided image.
Show that there will be no bound state unless 2mV0 / ħ ≥ π2 / 4.
(Hint: Note the similarity of this problem to the solution of the finite square well for the odd wave functions. )
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)
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
- Apply continuty conditions to prove the existence of probability for an electron to escape the boundaries when it is trapped in a finite potential well and discuss its energies, including the penetration depth using appropriate mathematical treatment.arrow_forwardin which ensembles ,open and closed assemblies are used?How can you connect lagrange undetermined multiplier with the Gibbs thermodynamic potential per system in grand canonical ensemble?arrow_forward(c) Consider a system of two qubits with canonical basis states {|0) , |1)}. Write down an example for a two- qubit density matrix corresponding to a separable pure state and an example for a two-qubit density matrix corresponding to an entangled pure state.arrow_forward
- 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_forwardConsider a particle confined to an infinite square potential well with walls at x = 0 and x = L. Calculate the probability of finding the particle in the n" energy eigenstate and somewhere in the first (1/a) th of the well (ie. in the region starting from one side of the well and extending L/a into the well).arrow_forwardA. at pattern. Let's ssuming that the e angular spatial poral frequencies w, correspond to e is then W, 1) ir) [7.33] avelength of the quals the group eing amplitude- e waves of fre- of modulating and sum over is called the wer sideband. 7.19 Given the dispersion relation w = ak', compute both the phase and group velocities. -7.20* Using the relation 1/v = dk/dv. prove that 1 Vg I V₂ 7.21* In the case of lightwaves, show that V = 1 Ve v dv v² dv V 7.22 The speed of propagation of a surface wave in a liquid of depth much greater than λ is given by v dn c dv 11 -+- C solve 7.25 only where g = acceleration of gravity, λ = wavelength, p = density. Y = surface tension. Compute the group velocity of a pulse in the long wavelength limit (these are called gravity waves). 7.23* Show that the group velocity can be written as dv dλ 7.24 Show that the group velocity can be written as gλ 2πΥ + 2πT pλ Vg = V-A ( n + w(dn/dw) 7.25 With the previous problem in mind prove that dn (v) dv n₂ = n(v) + v.…arrow_forward
- Using the nomalization constant A( nd the value of a evaluste the probability to find an escillator in the ground state 2h beyond the classical tuming points This problem cannot be solved in dlosed, analytic form. Develop an approximate, numerical method using a graph calculator, or computer. Assume an electron bound to an atomic-sized region (-0.1 m) with an effective force constant of 1.0 eVm. (To be marked comect, you must be within 25% of the corect answer)arrow_forwardProblem # 2. In the two-level system, estimate the emission line full width at half maximum (FWHM) for spontaneous emission at 650 nm if the spontaneous radiative lifetime of the upper state is about 3,000 nanoseconds.arrow_forwardAt what displacements is the probability density a maximum for a state of a harmonic oscillator with v = 1? (Express your answers in terms of the coordinate y.)arrow_forward
- Consider a d-functional potential well U(x) = -V8(x – a) o at | spaced by the distance a from an infinite potential barrier U(x) a < 0, as shown in the figure below. Obtain an equation for the energy level Eo of a bound state in the well. Using this equation, find the minimum distance ac of the well from the barrier at which the bound state in the well disappears for all a < ac. Infinite potential barrier a - Eo Energy level of a bound state U (x) = -V8(x – a) -arrow_forwardA 3-level system with degeneracies of 2, 3, 5 for its ground, first excited, and second excited states. Please write down its partition function.arrow_forwardTwo non-identical partic:les, each or mass m, arc confined in oe di- mension to an impenctrable box of length L. What irc the waıVe functions and energies of the three lowest-energy states of the system (i.c., in which at most one particle is excited out of its ground statc)? If an interaction potential of the form V12 = in A the energies of these three lowest states and] their wavc functions to zeroth order in A. A8(1 - r2) is added, calculate to first orderarrow_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