Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5, Problem 11CQ
(a)
To determine
To Sketch:The potential energy curve for the given particle.
(b)
To determine
The energy of the classical particle.
(c)
To determine
To Draw:The plot of E for a bound particle and indicate the outer classical turning point.
(d)
To determine
To Sketch:A plausible ground-state wave function
Expert Solution & Answer
Learn your wayIncludes step-by-step video
schedule06:14
Students have asked these similar questions
Write down the equations and the associated boundary conditions for
solving particle in a 1-D box of dimension L with a finite potential
well, i.e., the potential energy U is zero inside the box, but finite
outside the box. Specifically, U = U₁ for x L. Assuming that particle's energy E is less
than U, what form do the solutions take? Without solving the
problem (feel free to give it a try though), qualitatively compare with
the case with infinitely hard walls by sketching the differences in
wave functions and probability densities and describing the changes
in particle momenta and energy levels (e.g., increasing or decreasing
and why), for a given quantum number.
Consider the half oscillator" in which a particle of mass m is restricted to the region x > 0 by the potential energy
U(x) = 00
for a O
where k is the spring constant.
What are the energies of the ground state and fırst excited state? Explain your reasoning.
Give the energies in terms of the oscillator frequency wo =
Vk/m.
Formulas.pdf (Click here-->)
A particle of mass m moves in a three-dimensional box of sides a, b, c. If the potential is zero inside and infinity outside the box, find the energy eigenvalues and eigenfunctions.
Chapter 5 Solutions
Modern Physics
Ch. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQ
Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Prob. 13CQCh. 5 - Prob. 14CQCh. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Prob. 18CQCh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Obtain expression (5-23) from equation (5-22)....Ch. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - In a study of heat transfer, we find that for a...Ch. 5 - Prob. 73CECh. 5 - Prob. 74CECh. 5 - Prob. 75CECh. 5 - Prob. 76CECh. 5 - Prob. 77CECh. 5 - Prob. 78CECh. 5 - Prob. 79CECh. 5 - Prob. 80CECh. 5 - Prob. 81CECh. 5 - Prob. 82CECh. 5 - Prob. 83CECh. 5 - Prob. 84CECh. 5 - Prob. 85CECh. 5 - Prob. 86CECh. 5 - Prob. 87CECh. 5 - Prob. 88CECh. 5 - Consider the differential equation...Ch. 5 - Prob. 90CECh. 5 - Prob. 91CECh. 5 - Prob. 92CECh. 5 - Prob. 93CECh. 5 - Prob. 94CECh. 5 - Prob. 95CECh. 5 - Prob. 96CECh. 5 - Prob. 97CECh. 5 - Prob. 98CE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- We can use a quartic function function to represent this potential as shown below. Using the first order perturbation theory for particle in a box, calculate the ground- state energy: V(2) = ca 0< x < b a. How large of an effect on the energy is the perturbation of a curved wall?arrow_forwardA particle of mass m confined to an infinite potential well of length L from x= 0 to x=L is in the ground state. (a) Is this state an eigenfunction of the momentum operator, px? Justify your answer. (b) If an observation of momentum is made, what value, or values, could be obtained? Justify your answer.arrow_forward40. The first excited state of the harmonic oscillator has a wave function of the form y(x) = Axe-ax². (a) Follow thearrow_forward
- Demonstrate that e#ikz are solutions to both H and p, (momentum) for a free particle. Do you expect a difference for a bound particle where V (z) + 0?arrow_forwardUse the method of separation of variables to construct the energy eigenfunctions for the particle trapped in a 2D box. In other words, solve the equation: −ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y),−ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y), such that the solution is zero at the boundaries of a box of 'width' LxLx and 'height' LyLy. You will see that the 'allowed' energies EnEn are quantized just like the case of the 1D box. It is most convenient to to place the box in the first quadrant with one vertex at the origin.arrow_forwardLet's consider the two-qubit state 3 |) = 100)+101) +110). a) Find the expectation values for the values of both qubits separately. b) The product of qubit values is represented by the operator b₁b2 = (ô× 1) (I Øô) = (ô ❀ô), where bn is the observable for the value of qubit n. Find the expectation value for the product. For statistically independent quantities the expectation value of their product is the product of their expectation values. Are the values of the qubits correlated in state |V)? c) Show that the state cannot be expressed as a product state, i.e., it is an entangled state.arrow_forward
- (d) A linear perturbation A' = nx is applied to the system. What are the first order energy corrections to the energy eigenvalues E? (e) An anharmonic energy perturbation is applied to the system such that H' nx*. What %3D is the first order energy correction E for the ground state |0)? NOTE: Only do the ground state!!!arrow_forwardConsider the motion of a classical particle in a one dimensional double-well potential V(x) 1 (x? – 2). If the particle is displaced infinitesimally from the minimum on the x-axis (and friction is neglected), thenarrow_forwardPROBLEM 3. Using the variational method, calculate the ground state en- ergy Eo of a particle in the triangular potential: U(r) = 0 r 0. Use the trial function v(x) = Cx exp(-ar), where a is a variational parameter and C is a normalization constant to be found. Compare your result for Eo with the exact solution, Eo 1.856(h? F/m)/3.arrow_forward
- 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, .arrow_forwardWhat does your result for the potential energy U(x=+L) become in the limit a→0?arrow_forwardSuppose 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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax