Answered: 4) Is the function = B sin (bx) an…

4) Is the function = B sin (bx) an eigenfunction of the operator d/dx = = d/dx if B and b are constants and real numbers? Show your work in detail.

Physical Chemistry

2nd Edition

ISBN:9781133958437

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

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

Chapter10: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 10.40E

See similar textbooks

Related questions

Q: Find the eigenvalue of operating on the function f(x) = Asin(nx) + Bcos(mx) with the following…

Q: Evaluate the commutator [y², 82/8x² +82/8y2] by applying the operators to an arbitrary function f(x,…

A: To calculate the commutator for the operator y2, ∂2∂x2 +∂2∂y2 operating on an arbitrary function…

Q: 8. Calculate and for the particle in a 1-D box of length L described by: 4(x)=√(²) sin()

Q: Construct the potential energy operator of a particle with potential energy V(x)=1/2kfx2, where kf…

A: The information about the location of a particle is given by Born interpretation of the wave…

Q: 2. (a) Determine the normalization.constant for the particie in a box atypical wave function th…

A: A normalized wave function has Total probability over a integral with in limit is equal to one. A…

Q: (a) Consider a wavefunction of the form: =1+x-1<x<0 v(x) =1-x 0<x<1 i) Normalise the wavefunction…

A: To normalize the wavefunction, we need to determine the normalization constant A such that the…

Q: For a particle on a ring, how many nodes are there in the real part, and in the imaginary part of…

A: (i)

Q: Which of the following functions are eigenfunctions of the operator ·Â if Â = d² f(x)/dx²? Check all…

Q: Ch

Q: Sketch the form of the wavefunctions for the harmonic oscillator with quantum numbers v = 1 and 2.…

Q: Which of the following wavefunctions are eigenfunctions of the operator

Q: 4. Given these operators A=d/dx and B=x², can you measure the expectation values of the…

A: We have to use the concept of commutator over here. If the given observable commute with each other,…

Q: 3) Consider an arbitrary operator A. A operates on any function to its right. Here are the results…

A: Let an equation is, Âx = ax Where the operator(Â), operating on a function(x), produces a…

Q: The wavefunction for the motion of a particle on a ring is of the form ψ = Neimlϕ. Evaluate the…

A: For a normalized wavefunction, ∫ψ*ψ=1 where ψ is the wave function.

Q: Determine the commutator of the operators a and at. [₁,₂] = Â₁Â₂ - Â₂Î₁ at = (x- ip) √2 a = (X + ip)…

Q: Show that the wave function of a particle in a 1D box are mutually orthogonal to each other.

Q: 4) Which of the following functions are eigen functions of the operator dx? Show your proof. a) eax…

A: An eigenfunction of an operator is a function that, when the operator acts upon it, produces the…

Q: eigenstates

Q: Determine the domain of the function in the correct set notation. f(x)=. 1 2x+6 O {xx ER, x-3} O{xx…

A: The domain of a function is the set of all possible input values (often the 'x' variable), which…

Q: Find the eigenvalue of the function a° y°/3 when acted on by the operator Â = 2x + 2y- %3D dy

A: The operator which acts on a function and satisfies the following equation is called as an eigen…

Q: P17.4 Show a. that (x) = e Â = x² - 0²/ax²; and 2 ex²/2 is an eigenfunction of b. that B(x) (where Â…

Concept explainers

Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.

Question

4) Is the function = B sin (bx) an eigenfunction of the operator d/dx = = d/dx
if B and b are constants and real numbers?
Show your work in detail.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Techniques and Applications of Quantum Theory

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?
The following operators and functions are defined: A=x()B=sin()C=1()D=10()p=4x32x2q=0.5r=45xy2s=2x3 Evaluate: a Ap b Cq c Bs d Dq e A(Cr) f A(Dq)
Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue. a ddxcos4xb d2dx2cos4x c px(sin2x3)d x(2asin2xa) e 3(4lnx2), where 3=3f ddsincos g d2d2sincosh ddtan
For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?
Find the eigenvalue of operating on the function f(x) = Asin(nx) + Bcos(mx) with the following operator: P = d²/dx2 What must be the value of the constants A, B, m and n be to make the function an eigenfunction of this operator? 1.
3) Consider an arbitrary operator A. A operates on any function to its right. Here are the results of this operator on three different functions: Af(x, y, z) = hf(x, y, z) AY(0) = 04(0) ÂY(x) = Y(x) Which of the functions are eigenfunctions of Â?
Consider the operators d/dx and d²/dx². Is y (x) Aeikx an +Be-ikx eigenfunction of these operators? If so, what are the eigenvalues? A, B, and k are real numbers. =
please help and answe in details
2. Commuting operators. (a) Show whether the operator of the kinetic energy operator K and the momentum operator Px for a one-dimensional system commute (show every step). (b) What does the result mean (physical interpretation)?
(5) Demonstrate that the function p=-; d dx y = exp(timx) is simultaneously an eigenfunction of and p²
Which of the following functions are eigenfunctions of the momentum operator? a)eikx, b)eax2, c)x, d)x2, e)ax+b, d)sin(x+3a)Give the corresponding eigenvalue if appropriate.
(a) Consider a wavefunction of the form: =1+x-1