Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 38, Problem 16P
To determine
The proof that function
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For the scaled stationary Schrödinger equation "(x) + 8(x)v(x) = Ev(x),
find the eigenvalue E and the wave function ý under the constraint
/ »(x)²dx = 1.
Harmonic 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
2
The radial
function of a particle in
a central potential is give by
wave
[ -
r
R(r) = A-exp
where A is the normalization constant and a is positive constant
еxp
а
2a
of suitable dimensions. If ya is the most probable distance of the particle from the force
center, the value of y is
Chapter 38 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 38.3 - Prob. 1AECh. 38.8 - Prob. 1BECh. 38.8 - Prob. 1CECh. 38.9 - Prob. 1DECh. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Would it ever be possible to balance a very sharp...Ch. 38 - Prob. 6Q
Ch. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10QCh. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 17QCh. 38 - Prob. 18QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46GPCh. 38 - Prob. 47GPCh. 38 - Prob. 48GPCh. 38 - Prob. 49GPCh. 38 - Prob. 50GPCh. 38 - Prob. 51GPCh. 38 - Prob. 52GPCh. 38 - Prob. 53GPCh. 38 - Prob. 54GPCh. 38 - Prob. 55GPCh. 38 - Prob. 56GPCh. 38 - Prob. 57GPCh. 38 - Prob. 58GPCh. 38 - Prob. 59GP
Knowledge Booster
Similar questions
- (a) Show that the linear combination ‚E2 P(x, t) = 4; (x)e¯ +¥½(x)e¬l*t is a solution of the time-dependent Schrödinger equation, provided that the function W1 (x) and 2(x) are solutions of the time-independent Schrödinger equation with E = E, and E E2, respectively.arrow_forwardi) Why does the plane wave [Y(x,t)=Ae^i(kxewt)] have an issue and how to solve it? ii) What are the limitations of the time-dependent Schroedinger Equation?arrow_forward1) In Quantum Mechanics, the Laplacian operator operates upon wave function w in cartesian coordinate is as the following; v’y = By using curvilinear coordinate scale factors, show that the Laplacian operator operation in spherical coordinate is as the following; a( sine 1 d'y ' sin' 0 og or sin 0 ararrow_forward
- (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 correctarrow_forwardis this right?arrow_forward2) Consider a particle in a three-dimensional harmonic oscillator potential V (r, y, z) = 5mw²(r² + y² + z®). The stationary states of such a system are given by ntm(r, y, z) = vn(x)¢r(y)v'm(2) (where the functions on the right are the single-particle harmonic oscillator stationary states) with energies Entm = hw(n +l+m+ ). Calculate the lifetime of the state 201.arrow_forward
- 1. Infinite-Potential Well Revisited V(x) V = 0 V = 0 V = 0 L x = 2 x = +5 2 Consider the quantum mechanics of a particle with mass m that is confined in the infinit potential well of width L as shown above. (a) By direct substitution into the time-independent Schrödinger, h? d²µ(x) +V(x)µ(x) = EÞ(x) 2m dx? show that the wavefunction of the particle is Pn(x) = Asin + with the quantized energy levels given by h?n²n? E = En = 2ml? where n = 1,2,3, ...arrow_forwardA 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 3mhwarrow_forwardCan the magnitude of a wave function (*(x,t)(x,t)) be a negative number? Explain.arrow_forward
- Can we simultaneously measure position and energy of a quantum oscillator? Why? Why not?arrow_forward(a) Derive an expression for the variance in the number of particles in a state for a Bose- Einstein gas when the number of particles in the gas can change. (b) Using the particle number for the Bose-Einstein gas, determine any specific properties of the chemical potential.arrow_forward(i) We consider a one-dimensional potential barrier problem. In order for the particle to tunnel through the potential barrier of the width L, the difference between the barrier height U and the incident energy E of the particle with mass m has to be close. Using the transmission probability given in the text book / lecture, obtain the energy difference U-E which gives the transmission probability of exp(-2). (ii) We consider an infinite square well potential with the width L. Obtain the energy E_{gr} of the lowest energy level (ground state) of the particle with mass m, and show that E_{gr} scales linearly with E-U in the problem (i). The potential structures of (i) and (ii) can be viewed as "shadows" of each other. Energy U ---E« Electron X L L (iii) We now consider a 3-dimensional infinite square well potential having the length of the x, y, and z directions to be all L. V=L**3 is the volume of the cube of this potential. We consider energy level of a single particle (boson)…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning