Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Question
Chapter 6, Problem 49E
To determine
Time require for an electron to reach length of an automobile
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Students have asked these similar questions
A particle is confined to a one dimensional box with boundaries at x=0 and x-1. The wave
function of the particle within the box boundaries is V(x)
2100 (-
x + ) and zero
V 619
everywhere else. What is the probability of finding the particle between x=0 and x=0.621? Do
not enter your final answer as a percentage, but rather a number between 0 and 1. For
instance, if you get that the probability is 20%, enter 0.2.
An electron with an initial kinetic energy of 1.542 eV (in a region with 1.095 eV potential energy) is incident on a potential step (extending from x=0 to ∞) to V=2.381 eV. What is the transmission probability (in %)? FYI: If we had a travelling wave arriving at a similar potential DROP, then k1 (for x<0) would be real and the symmetry of R=(k1-k2)2/(k1+k2)2 implies reflection/transmission are the same as a potential RISE with the same energies but k1 and k2 swapped.
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 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
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- Consider a quantum particle with energy E approaching a potential barrier of width L and heightV0 > E from the right (as shown in image). The wavefunction of the particles in the region x > L is given by ψ = A exp {−i (kx + ωt)} , where A, k and ω are all constants. Use the Gamow factor formalism to calculate an approximate expression for the transmission rate of these particles through the barrier.arrow_forwardFor the same system as in Exercise E7C.4(a) (Functions of the form cos(nπx/L), where n = 1, 3, 5 …, can be used to model the wavefunctions of particles confined to the region between x = −L/2 and x = +L/2. The integration is limited to the range −L/2 to +L/2 because the wavefunction is zero outside this range. Show that the wavefunctions are orthogonal for n = 1 and 3. You will find the necessary integral in the Resource section), show that the wavefunctions with n = 3 and 5 are orthogonal.arrow_forwardThe wave function of free particle initially at time t=0 is given by the wave packet $(x,0) = [2π(4x)3]-¹/4 exp{-4(4x)³ ikox} + ik where (Ax) represents the initial width of the wave packet (i.e. the variance). a) (x, t). b) Determine the wave function for the free particle at some later time t, What is the width (the variance) of the wave packet at the later time t?arrow_forward
- Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).arrow_forwardConsider a particle in a box of length L with one end coinciding with the origin. Compute the time-dependent uncertainty in position and momentum for a particle that is in an equal probability superposition of the n =1 and n = 3 states. Demonstrate the Heisenberg uncertainty relations in this case.arrow_forwardProblem 1: (a) A non-relativistic, free particle of mass m is bouncing back and forth between two perfectly reflecting walls separated by a distance L. Imagine that the two oppositely directed matter waves associated with this particle interfere to create a standing wave with a node at each of the walls. Find the kinetic energies of the ground state (first harmonic, n = 1) and first excited state (second harmonic, n = 2). Find the formula for the kinetic energy of the n-th harmonic. (b) If an electron and a proton have the same non-relativistic kinetic energy, which particle has the larger de Broglie wavelength? (c) Find the de Broglie wavelength of an electron that is accelerated from rest through a small potential difference V. (d) If a free electron has a de Broglie wavelength equal to the diameter of Bohr's model of the hydrogen atom (twice the Bohr radius), how does its kinetic energy compare to the ground-state energy of an electron bound to a Bohr model hydrogen atom?arrow_forward
- A particle in a box is in the ground level. What is the probability of finding the particle in the right half of the box? (Refer to Fig. , but don’t evaluate an integral.) Is the answer the same if the particle is in an excited level? Explain.arrow_forwardGiven: For sake of simplicity, let us consider a particle with mass, m, in one dimension trapped in an infinite square well potential. The bottom of the potential well has zero potential energy, and the particle is known to be confined between 0arrow_forwardConsider a beam of particles which is incident on a potential barrier, and assume that the potential-energy function is constant in the domains of the incident and transmitted beams. The wavefunctions representing incident, reflected and transmitted particles are given by V:(1, t) = Ae (k12–wit), V.(x,t) = Be¬i(k12+wit) and V.(x,t) = Ce(ka=–-wat), respectively. a) The current density is defined by J = 2mi Calculate the incident, reflected and transmitted current densities (J;, J,, and Jt, respectively). b) Express the transmission coefficient T = |Jt/J;| and the reflection coefficient R = |Jr/J;| in terms of A, B, C, ki and k2.arrow_forwardShow that the probability of obtaining En for a particle in a box with the provided wave function (see first image) is given by the equation in the first image. Hint: The probability of obtaining the ground-state energy E1 is determined in Example 3.4, as shown in the second provided image.arrow_forwardU = U, %3D U = 0 X = 0 A potential step U(x) is defined by U(x) = 0 for x 0 If an electron beam of energy E > U, is approaching from the left, write the form of the wave function in region I (x 0) in terms of the electron mass m, energy E, and potential energy U,. Do not bother to determine the constant coefficients. Formulas.pdf (Click here-->) Edit Vicw Insert Format Tools Table 12pt v Paragraph BIU Av eu T? varrow_forwardShow that the wavelength predicted for a particle in a one-dimensional box of length L from the de Broglie relationship matches the wavelength predicted from solutions of the corresponding Schrödinger equation where the potential is defined as: 6. E V(x)=0 (barrier) V(x)=0 (well) V(x)=∞ (barrier) (Hint: You can do this for any value of n you want although we recommend the n=2 case).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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