Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term
10th Edition
ISBN: 9781337888516
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 15P
(a)
To determine
To show that
(b)
To determine
The energy of the particle.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
The wave function of a quantum particle of mass m is ψ(x) = A cos (kx) + B sin (kx)where A, B, and k are constants. (a) Assuming the particle is free (U = 0), show that ψ(x) is a solution of the Schrödinger equation (as shown). (b) Find the corresponding energy E of the particle.
Let Ψ (x, t) = (A / (a2 + x2)) exp (-i 2 π E t / h ) be a normalized solution to Schrodinger’s equationfor constants A, a, and E.(a) What is A in terms of a?(b) What is the potential function V(x)?(c) Evaluate Δx Δp. Is the uncertainty principle satisfied?
Show that the wave function ψ = Ae i(i-ωt) is a solution to the Schrödinger equation (as shown), where k = 2π/λ and U = 0.
Chapter 40 Solutions
Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.5 - Prob. 40.4QQCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6P
Ch. 40 - Prob. 7PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 13PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Two particles with masses m1 and m2 are joined by...Ch. 40 - Prob. 31APCh. 40 - Prob. 32APCh. 40 - Prob. 33APCh. 40 - Prob. 34APCh. 40 - Prob. 36APCh. 40 - Prob. 37APCh. 40 - Prob. 38APCh. 40 - Prob. 39APCh. 40 - Prob. 40APCh. 40 - Prob. 41APCh. 40 - Prob. 42APCh. 40 - Prob. 44CPCh. 40 - Prob. 46CPCh. 40 - Prob. 47CP
Knowledge Booster
Similar questions
- A particle of mass m is confined to a 3-dimensional box that has sides Lx,=L Ly=2L, and Lz=3L. a) Determine the sets of quantum numbers n_x, n_y, and n_z that correspond to the lowest 10 energy levels of this box.arrow_forwardQ.54 A particle in one dimensional box of length 2a with potential energy [0 1지 a V = is perturbed by the potential V'= cx eV, where c is a constant. The 1st order correction to the 1st excited state of the system is хсeV.arrow_forwardWhat is the value N so that ψ(x) = N/(a2 + x2) can give rise to a valid probability density?arrow_forward
- Solving 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_forwardThe general solution of the Schrodinger equation for a particle confined in an infinite square-well potential (where V = 0) of width L is w(x)= C sin kx + Dcos kx V2mE k where C and D are constants, E is the energy of the particle and m is the mass of the particle. Show that the energy E of the particle inside the square-well potential is quantised.arrow_forwardA particle of mass m is moving in an infinite 1D quantum well of width L. y,(x) = J? sinx. sin nAx L (a) How much energy must be given to the particle so it can transition from the ground state to the second excited state? (b) If the particle is in the first excited state, what is the probability of finding the particle between x = and x = ;? 2.arrow_forward
- An electron has a wavefunction ψ(x)=Ce-|x|/x0 where x0 is a constant and C=1/√x0 for normalization. For this case, obtain expressions for a. ⟨x⟩ and Δx in terms of x0. b. Also calculate the probability that the electron will be found within a standard deviation of its average position, that is, in the range ⟨x⟩-∆x to ⟨x⟩+∆x, and show that this is independent of x0.arrow_forwardThe wave function ψ(x) = Bxe-(mω/2h)x2is a solution to the simple harmonic oscillator problem. (a) Find the energy of this state. (b) At what position are you least likely to find the particle? (c) At what positions are you most likely to find the particle? (d) Determine the value of B required to normalize the wave function. (e) What If? Determine the classical probability of finding the particle in an interval of small length δ centered at the position x = 2(h/mω)1/2. (f) What is the actual probability of finding the particle in this interval?arrow_forward(a) Write the relevant form of Schrödinger equation for the free particle. (b) Consider a quantum particle of mass m with the wave function given as 4(x) = A tan(kx), where A and k are constants. Verify if 4(x) is the solution of the Schrödinger's equation written in part-(a).arrow_forward
- A proton has the wave function (Capital_Psi)(x) = Ae^(-x/L) with total energy equal to one-seventh its potential energy. What is the potential energy (in eV) of the particle if the wave function satisfies Schrodinger's equation? Here L = 3.80 nm.arrow_forward11:44 ← SPHA031-23 Assignm... SPHA031 Assignment No 3 o Vo 4G+ LTE2 T 1. A particle is confined in a region 0≤x≤ ∞o and has a wavefunction of the form = Ne-xa ||| (a) Normalize the wave function. (b) Find the average position of the article. (c) Find the average momentum of the particle. (d) Show that the uncertainties in position and momentum of the particle are given by 1 Ax = = and Ap = 0. 2a 2. The Heisenberg uncertainty principle demonstrate the symmetry between the particles position and momentum. This can further be extended to the particles probability amplitudes in position (x, t) and momentum (p, t). If y(x, t) = 1 √27th S dp (p, t)ex is the Fourier expansion of the probability amplitude for position and (p,t)=√x 4(x, t)ex is its Fourier transform, prove that +4(x, t) |² dx = +|ỹ(p,t)|²dp. 2arrow_forwardAn electron is trapped in a one-dimensional region of length 1.00 x 10-10 m (a typical atomic diameter). (a) Find the energies of the ground state and first two excited states. (b) How much energy must be supplied to excite the electron from the ground state to the sec- ond excited state? (c) From the second excited state, the electron drops down to the first excited state. How much energy is released in this process?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning