Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 4, Problem 52E
(a)
To determine
The expression for the total energy of the particle in terms of its position, mass, momentum and the force constant.
(b)
To determine
The expression for the total energy of the particle in terms of its position.
(c)
To determine
The minimum possible energy of the wave.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Consider a collision between cart A, moving at speed, and cart B, immobile. The masses of the carts are known, as well as their uncertainty. Friction is neglected.
Using the conservation of energy theorem, program cells to predict the speed of sliders A and B after the collision as well as its uncertainty.
mA=(0.47±0.05) kg
mB=(0.47±0.06) kg
vi A=(1.9±0.02) m/s
An electron is revolving around a proton in a circular orbit of radius r. The proton is assumed to be
stationary. The total energy of this system is
p? 1 e?
E
2m 4TE, r
where p and m denote the momentum and mass of the electron, respectively. Take the radius r to be an estimate
of the uncertainty in position Ar, and the uncertainty in momentum Ap to be an estimate of p. Suppose that
ArAp = ħ when the system is in the ground state.
Show that the ground state energy is given by
1 me4
e 8h?
E1
Give the numerical value for E, in electronvolts. Discuss if your results are consistent with Bohr's model for
the hydrogen atom.
Problem 1. Using the WKB approximation, calculate the energy eigenvalues En of a quantum-
mechanical particle with mass m and potential energy V (x) = V₁ (x/x)*, where V > 0, Express
En as a function of n; determine the dimensionless numeric coefficient that emerges in this
expression.
Chapter 4 Solutions
Modern Physics
Ch. 4 - Prob. 1CQCh. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Prob. 5CQCh. 4 - Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - Prob. 10CQ
Ch. 4 - Prob. 11ECh. 4 - Analyzing crystal diffraction is intimately tied...Ch. 4 - The setup depicted in Figure 4.6 is used in a...Ch. 4 - Prob. 14ECh. 4 - Prob. 15ECh. 4 - Prob. 16ECh. 4 - Prob. 17ECh. 4 - Prob. 18ECh. 4 - Prob. 19ECh. 4 - Prob. 20ECh. 4 - Prob. 21ECh. 4 - Prob. 22ECh. 4 - Prob. 23ECh. 4 - Prob. 24ECh. 4 - Prob. 25ECh. 4 - Prob. 26ECh. 4 - Prob. 27ECh. 4 - Prob. 28ECh. 4 - Prob. 29ECh. 4 - Prob. 30ECh. 4 - Prob. 31ECh. 4 - Prob. 32ECh. 4 - Prob. 33ECh. 4 - Prob. 34ECh. 4 - Prob. 35ECh. 4 - Prob. 36ECh. 4 - Prob. 37ECh. 4 - (a) Experiment X is carried out nine times...Ch. 4 - Prob. 39ECh. 4 - Prob. 40ECh. 4 - Prob. 41ECh. 4 - Prob. 42ECh. 4 - Prob. 43ECh. 4 - Prob. 44ECh. 4 - Prob. 45ECh. 4 - Prob. 46ECh. 4 - Prob. 47ECh. 4 - Prob. 48ECh. 4 - Prob. 49ECh. 4 - Prob. 50ECh. 4 - Prob. 51ECh. 4 - Prob. 52ECh. 4 - Prob. 53ECh. 4 - Prob. 54ECh. 4 - Prob. 55ECh. 4 - Prob. 56ECh. 4 - Prob. 57ECh. 4 - Prob. 59ECh. 4 - Prob. 60ECh. 4 - Prob. 61ECh. 4 - Prob. 62ECh. 4 - Prob. 63ECh. 4 - Prob. 64ECh. 4 - Prob. 65ECh. 4 - Prob. 67ECh. 4 - Prob. 68ECh. 4 - Prob. 71CECh. 4 - Prob. 72CECh. 4 - Prob. 73CE
Knowledge Booster
Similar questions
- An electron is confined to a region of space of the size of an atom (0.1 nm). (a) What is the uncertainty in the momentum of the electron? (b) What is the kinetic energy of an electron with a momentum equal to Ap? (c) Does this give a reasonable value for the kinetic energy of an electron in an atom?arrow_forwardCompute the uncertainty of 1/x in terms of x and its uncertainty, δx .arrow_forwardAn electron is revolving around a proton in a circular orbit of radius r. The proton is assumed to be stationary. The total energy of this system is p2 E e2 2m 4T€, r where p and m denote the momentum and mass of the electron, respectively. Take the radius r to be an estimate of the uncertainty in position Ar, and the uncertainty in momentum Ap to be an estimate of p. Suppose that ArAp involving only m, e, ħ, and €o. Give the numerical value for E1 in electronvolts. Discuss if your results are consistent with Bohr's model for the hydrogen atom. h when the system is in the ground state. Obtain the expression for the ground state energy E1,arrow_forward
- Consider a particle of mass m moving in a 2-dimensional rectangular box of sides La and Ly, with Le 2Ly. If we use the symbols E, to denote the energy of the ground state of the system, Ee1 the energy of the first excited state, Ee2 the energy of the second excited state, and Ee3 the energy of the third excited state, what are the numerical values of the ratios Ee1/Eg, Ee2/Eg, and Ee3/E,?arrow_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_forwardV (x) = 00, V(x) = 0, x<0,x 2 a 0arrow_forwardx + 5 x 5 Calculate the following values: a. q( – 3) : b. q(7) = q(5) = C.arrow_forward8. Classical Mechanics. The differential equation for the velocity v of an object of mass m, restricted to vertical motion and subject only to the forces of gravity and air resistance, is dv (1) m -mg - yv. dt In Eq. (i) we assume that the drag force, -yu where y> 0 is a drag coefficient, is proportional to the velocity. Acceleration due to gravity is denoted by g. Assume that the upward direction is positive. (a) Show that the solution of Eq. (i) subject to the initial condition v(0) = vo is mg mg V= vo + mo) e e-rt/m Y (b) Sketch some integral curves, including the equilibrium solution, for Eq. (i). Explain the physical significance of the equilibrium solution. (c) If a ball is initially thrown in the upward direction so that vo > 0, show that it reaches its maximum height when m Yvo t = tmax (1 + Y mg -Inarrow_forwardConsider the following variables with their mean and uncertainties specified: X= 37.2 +/- 1.5 m Y= 31.1 +/- 0.6 m T= 4.34 +/- 0.05 s Find the propagated errors in the following functions that depend on these variables. F=T? V= 5X/T G=Exp {10X/Y} W=X/T+Y/Tarrow_forwardA student performs the experiment and measures the distance between photogates: d = 50 ± 0.1 cm, the times measured by photogates: t0 = 0.052 ± 0.001s and t1 = 0.035 ± 0.001s, and the cart’s length: s = 10 ± 0.05 cm. Find the acceleration a of the cart and estimate uncertainty in a.arrow_forwardConsider a one-dimensional particle which is confined within the region 0≤x≤a and whose wave function is (x, t) = sin (x/a) exp(-iwt). (D) v sv (a) Find the potential V(x). (b) Calculate the probability of finding the particle in the interval a/4 ≤x≤3a/4.arrow_forwardConsider a physical quantity q=2a+ 3b-4c, and a = 50 +2.5, b = 25 +3.1 and c = 80 +3.5 and a, b and c are random and independent, what is the value and absolute uncertainty of q?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning