Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 88CE
(a)
To determine
The variation of the potential energy and the wave function of the particle.
(b)
To determine
The probability that the particle would be found in the classically forbidden region.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(2nx
sin
\1.50.
2nz
Consider the case of a 3-dimensional particle-in-a-box. Given: 4 =
sin(ny) sin
2.00.
What is the energy of the system?
O 6h?/8m
O 4h²/8m
O 3h2/8m
O none are correct
A particle of massm in a harmonic oscillator potential with angular frequency w is in the state
(1 + {t)쭈
What is (p?) for this particle?
mhw
2
O 6mħw
O 3mhw
5. A particle of mass m in a rectangular box with dimensions x, y, z has ground
k² ( 1
1
+
y?
1
state energy E(x, y, z) =
where k is a physical constant. If
+
8m x
the volume of the box is fixed (say V =xyz ), find the values of x, y, and z that
minimize the ground state energy.
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
Similar questions
- Consider an anisotropic 3D harmonic oscillator where we = Wy the energy of the particle in the following state (nx, ny, n₂) = (0, 0, 2)? = w and wz A. 4ħw B. 6hw C. 3ħw D. 2.5ħw = 2w. What isarrow_forward+8 x a nd described by the wave function y(x)= Bsin(kx). Determine i) The energy levels, the omentum, the wave length, the parity and number of nodes for the states n = 1, 2 3 and 4. Suppose V=10 J in the box. What effect has this on a) eigenvalues? b) the eigen functions?arrow_forwardA particle with mass m is in the state тс V (x,t) = Ae +iat 2h where A and a are positive real constants. Calculate the potential energy function that satisfies the Schrodinger equation.arrow_forward
- Suppose a particle of mass m is moving in a one-dimensional potential of a kind -24arrow_forwardQuestion 1. An electron with a total energy E moves in a 1-D region 1. At x=0, there is a potential energy step of height V. (as shown in the figure 2). Where the wave functions 41(x) = Aelax+ Be-iax, 42(x) = Ce-x/b+ Dex/b 1) H) Find the real numbers a and b in terms of E and Vo. State whether the electron energy is greater than or less than VO and why. Incident particles Region I V(x) Vo x=0 Region II Figure 2. Step potential functionarrow_forwardAn electron (m = 9.109*10^-31 kg) is confined in a one-dimensional infinite square well of width L = 10 nm. determine energy for first excited energy statearrow_forward24. Consider a modified box potential with V(x) = V₁x, Vi(ar), x a Use the orthogonal trial function = c₁f₁+c₂f₂ with f₁ = √√sin (H) and f2 = √√ √√sin sin (2) to determine the upper bound to ground state energy.arrow_forwardYou want to determine the possible energy observable values of a particle in a non- zero potential described by a wave function. Which of the following equations represents that process? ħ² 2m ·V² + V| y = 0 +17] 26 οψ ħ² [2²] =0 &= 04 2m – iħ√y = oy xy = 06arrow_forwardHarmonic oscillator eigenstates have the general form 1 μω ,1/4 μω AG)(√(-) n ħ In this formula, which part determines the number of nodes in the harmonic oscillator state? = y (x) 1 √(™ ћn 2"n! Holev 1/4 μω 1 2"n! exp(-1022²) 2ħ μω ħ 2"n! exp μω χ 2ħ 2arrow_forwardSolving the Schrödinger equation for a particle of energy E 0 Calculate the values of the constants D, C, B, and A if knownCalculate the values of the constants D, C, B, and A if known and 2mE 2m(Vo-E) a =arrow_forwardA particle is confined in a box of length L as shown in the figure. If the potential is treated as a perturbation, including the first order correction, the ground state energy is (a) E = ħ²π² 2mL² + V (b) E = ħ²π² Vo 2mL² ħ²π² Vo ħ²π² Vo (c) E = + (d) E = + 2mL² 4 2mL² L/2arrow_forwardA proton is in a one-dimensional box of width 7.8 pm (1 pm = 1 x 10-¹2 m). The energy of the proton is equal to the absolute value of the ground state of a hydrogen atom. What state is the proton in?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning