This is from a study guide for a final, not a graded assignment. 3. Which function(s) is/are eigenfunctions of the operatora²?3x²Iax² + b=1acos(bx)aeixIV xcos(bx)a. I onlyb. II and IIIc. II and IVd. Ill onlyto of

Step 1: Step 2: Step 3: Step 4:

Answered: 3. Which function(s) is/are…

Introductory Chemistry: A Foundation

9th Edition

ISBN:9781337399425

Author:Steven S. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Donald J. DeCoste

Chapter10: Energy

Section: Chapter Questions

Problem 3QAP

See similar textbooks

Similar questions

Indicate which of these expressions yield eigenvalue equations, and if so indicate the eigenvalue. a ddxsinx2b d2dx2sinx2 c iddxsinx2d iddxeimx, where m is a constant e ddx(ex)f (22md2dx2+0.5)sin2x3 g ddy(ey2)
A particle of mass m is placed in a three-dimensional rectangular box with edge lengths 2L, L, and L. Inside the box the potential energy is zero, and outside it is infinite; therefore, the wave function goes smoothly to zero at the sides of the box. Calculate the energies and give the quantum numbers of the ground state and the first five excited states (or sets of states of equal energy) for the particle in the box.
(a) Using Equation 4.36, make a graph of the n=3 wave function and the square of this wave function for a particle in a box with the edges at x=0 and x=7 . Estimate the probability of finding the particle between x1=3 and x2=4 . You may either do an integral or find the area under the curve by counting the number of rectangular boxes (roughly estimating the fractional boxes), and then multiply by the area of each box, watching your units. Show your calculation with units for credit. (b) Verify that the n=3 wave function in (a) is an allowed quantum state (sometimes called an eigenfunction) of by substituting it for in the left side of the equation =E immediately following Eq. 4.32. Calculate the derivatives to see if your result E is a constant multiplied by the original n=3 wavefunction. What does the constant you get tell you about the energy of thiseigenstate? Is it in agreement with the energy for the n=3 level you would calculate from Equation 4.37?
How many nodal planes exist for a 5d orbital? (a) 0 (b) 1 (c) 2 (d) 3
5. Which is true about the function 5sin(5x) and the operator d?/dx2? a. The function 5sin(5x) is an eigenfunction of the operator d?/dx² and the eigenvalue is 125. b. The function 5sin(5x) is an eigenfunction of the operator d?/dx² and the eigenvalue is -25. c. The function 5sin(5x) is an eigenfunction of the operator d?/dx² and the eigenvalue is -125. d. The function 5sin(5x) is an eigenfunction of the operator d?/dx² and the eigenvalue is 25. e. The function 5sin(5x) is not an eigenfunction of the operator d?/dx?. 6. If the maximum kinetic energy of photoelectrons is 0.80 hv, then a. radiation of frequency v/0.8 will not cause a photoelectric effect. b. doubling the intensity of the radiation will cause the ejection of electrons with the maximum kinetic energy of 1.60 hv. c. radiation of frequency 2v will cause a photoelectric effect; the ejected electrons have a maximum kinetic energy of 1.60 hv. d. the work function of the metal is 0.80 hv. None of the given statements is correct.…
d? A = 4x² 3. Given the operator dx? determine the value of k that makes the wave function v (x)= e** an eigenfunction of 4
2. Which of the following wavefunctions are eigenfunctions of the momentum operator? For those that are eigenfunctions of momentum, what is the corresponding eigenvalue? a. Ae+ b. cos ax +i3x c. sin? x
2. For the following functions and operators, determine if the given function is an eigenfunction of the operator. If the function is an eigenfunction, determine the eigenvalue of the operator. a. Ĥ (V=0), y = A sin(nx²) b. p, y=B exp{-ikx} c. x, y = c ( 1⁄₂ - 1) C ə ô - (ax + by), w = дх d. ô y = K x²y²
dxz (. 15 sine cose coso) is an eigenfunction of l, OT
Is the function w(x) = sinx an eigenfunction for the linear momentum operator, 6.? If yes, what is the eigenvalue? O Yes, the eigenvalue is -1 Yes, the eigenvalue is sinx O Yes, the eigenvalue is – in O No
The eigenvalue of the Hamiltonian operator Cof the following function H 3ix2 y=2e O A.72x 2x e 3ix? O B. - 72x? OCy is not an eigenfunction of H O D. -72
Consider the angular momentum operator Îz in coordinate representation L₂ = − iħ (x ² − y ²²x), a. express Î₂ in spherical coordinates. b. what are the (unnormalized) eigenfunctions? c. what normalization condition do these eigenfunction satisfy? d. what are the eigenvalues Lz?

SEE MORE QUESTIONS

Recommended textbooks for you

Introductory Chemistry: A Foundation

Chemistry

ISBN:

9781337399425

Author:

Steven S. Zumdahl, Donald J. DeCoste

Publisher:

Cengage Learning

Physical Chemistry

Chemistry

ISBN:

9781133958437

Author:

Ball, David W. (david Warren), BAER, Tomas

Publisher:

Wadsworth Cengage Learning,

Organic Chemistry: A Guided Inquiry

Chemistry

ISBN:

9780618974122

Author:

Andrei Straumanis

Publisher:

Cengage Learning

Introductory Chemistry: A Foundation

Chemistry

ISBN:

9781337399425

Author:

Steven S. Zumdahl, Donald J. DeCoste

Publisher:

Cengage Learning

Physical Chemistry

Chemistry

ISBN:

9781133958437

Author:

Ball, David W. (david Warren), BAER, Tomas

Publisher:

Wadsworth Cengage Learning,

Organic Chemistry: A Guided Inquiry

Chemistry

ISBN:

9780618974122

Author:

Andrei Straumanis

Publisher:

Cengage Learning

Chemistry: Principles and Practice

Chemistry

ISBN:

9780534420123

Author:

Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Publisher:

Cengage Learning

Principles of Instrumental Analysis

Chemistry

ISBN:

9781305577213

Author:

Douglas A. Skoog, F. James Holler, Stanley R. Crouch

Publisher:

Cengage Learning

Chemistry & Chemical Reactivity

Chemistry

ISBN:

9781133949640

Author:

John C. Kotz, Paul M. Treichel, John Townsend, David Treichel

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

3. Which function(s) is/are eigenfunctions of the operator a² ? 3x² I ax² + b = 1 acos(bx) aeix IV xcos(bx) a. I only b. II and III c. II and IV d. Ill only to of