PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
6th Edition
ISBN: 9781429206099
Author: Tipler
Publisher: MAC HIGHER
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 35, Problem 33P
(a)
To determine
Prove that the wave numbers
(b)
To determine
Prove that the reflection coefficient is
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A O, molecule oscillates with a frequency of 4.7 x1013 Hz.
(a) What is the difference in energy in ev between allowed oscillator states?
ev
(b) what is the approximate value of n for a state having an energy of 1.4 eV? (Give your answer to the nearest integer.)
Consider a particle moving in a one-dimensional box with walls at x = -L/2 and L/2.
(a) Write the wavefunction and probability density for the state n=1.
(b) If the particle has a potential barrier at x =0 to x = L/4 (where L = 10 angstroms) with a height of 10.0 eV, what would be the transmission probability of the electrons at the n = 1 state?
(c) Compare the energy of the particle at the n= 1 state to the energy of the oscillator at its first excited state.
Calculate the transmission probability for quantum-mechanical tunneling in each of the following cases. (a) An electron with an energy deficit of U - E= 0.010 0 eV is incident on a square barrier of width L = 0.100 nm. (b) An electron with an energy deficit of 1.00 eV is incident on the same barrier. (c) An alpha particle (mass 6.64 × 10-27 kg) with an energy deficit of 1.00 MeV is incident on a square barrier of width 1.00 fm. (d) An 8.00-kg bowling ball withan energy deficit of 1.00 J is incident on a square barrier of width 2.00 cm.
Chapter 35 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
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
- Consider two identical conducting wires, lying on the x axis and separated by an air gap of thickness L=1nm. The work function of the metal is W=5 eV. (a) Find the probability that the electron will emerge on the other side of the barrier? (b) Find the electric field needed to allow the tunneling probability of 10-5.arrow_forward6QM Please answer question throughly and detailed.arrow_forwardAn electron with kinetic energy E = 3.10 eV is incident on a barrier of width L = 0.230 nm and height U = 10.0 eV (a) What is the probability that the electron tunnels through the barrier? (Use 9.11 10-31 kg for the mass of an electron, 1.055 ✕ 10−34 J · s for ℏ, and note that there are 1.60 ✕ 10−19 J per eV.) b) What is the probability that the electron is reflected? What If? For what value of U (in eV) would the probability of transmission be exactly 25.0% and 50.0%? c) 25.0% d) 50.0%arrow_forward
- a) If the electron is in the ground state argue that the expectation value of the electric dipole (P.) =(qf) must vanish. Do not need to do a calculation. b) Show that for some of the n=2 states the expectation value (p,)=(qî) does not vanish. Give one example and proceed to calculate that expectation value.arrow_forwardConsider a system in a state Y If the x component of 2, m angular momentum L is measured on it, find the possible values the measurement will yield and their correponding probabilities.arrow_forwardpls answer d and earrow_forward
- 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)arrow_forwardAn electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. Quantum- mechanically, however, the probability of tunneling is not zero. (a) Calculate this probability, which is the transmission coefficient. (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.50-eV electron tunneling through the barrier to be one in one million?arrow_forwardb) Consider a particle in a superposition state with the wave function Ru >Y the ware unebiongle, fhad the i) Depine Normalize constant A. What is the probability that a measurement of Lz will yield a value Lz = 0? Find the expectation values of L2arrow_forward
- The coherent states for the one-dimensional harmonic oscillator are defined as eigenstates of the operatorof annihilation a (which is non-Hermitian):a |λ⟩ = λ |λ⟩ (1)where λ is a complex number in general. a)prove that is a normalized consistent state. b)Show that the above state satisfies the minimum uncertainty relation, i.e., show thatarrow_forwarda) In the postulates of Quantum Mechanics, explain superposition principle and expectation value of an observable.(b) Establish the quantum mechanical operators for the component of angular moment in Cartesian coordinate system.arrow_forwardIn a simple model for a radioactive nucleus, an alpha particle (m = 6.64 * 10-27 kg) is trapped by a square barrier that has width 2.0 fm and height 30.0 MeV. (a) What is the tunneling probability when the alpha particle encounters the barrier if its kinetic energy is 1.0 MeV below the top of the barrier (Fig. )? (b) What is the tunneling probability if the energy of the alpha particle is 10.0 MeV below the top of the barrier?arrow_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
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning