Answered: 4. Given these operators A=d/dx and…

4. Given these operators A=d/dx and B=x², can you measure the expectation values of the corresponding observables to infinite precision simultaneously?

Physical Chemistry

2nd Edition

ISBN:9781133958437

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

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

Chapter12: Atoms And Molecules

Section: Chapter Questions

Problem 12.21E

See similar textbooks

Related questions

Q: For a particle in the stationary state n of a one dimensional box of length a, find the probability…

Q: P= D„Ðx= (-in- Assume that -in- dx dx dx2 Evaluate for a particle in a box with 0 =m?v² h?n? II

A: This question comes under quantum mechanics and the topic is evaluation of average value for…

Q: Consider an operator O having f(x) and g(x) as its eigenfunctions producing the same eigenvalue o.…

Q: Vanadium tetrachloride (VCl4 ) is a bright red colored liquid with a vapor pressure of 5x10-2 torr…

A: The orbital angular momentum of electron inn a given orbital is calculated by using the following…

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: For a particle in a box of length L and in the state with n = 3, at what positions is the…

A: The wavefunction does not describe exact location of the microscopic particle. It tells about…

Q: Show that the third Bohr postulate, Eq. (2–5), is equivalent to an integer num- ber of de Broglie…

A: Bohr᾿s Postulate states that, An electron should revolve round only certain specified circular orbit…

Q: The wavefunction of one of the d orbitals is proportional to cos θ sin θ cos ϕ. At what angles does…

Q: A particle freely moving in one dimension x with 0 ≤ x ≤ ∞ is in a state described by the normalized…

A: Given normalized wave function ψ(x) = a1/2e–ax/2 where 'a' is a constant. Particle freely moving in…

Q: d? A = 4x² 3. Given the operator dx? determine the value of k that makes the wave function v (x)=…

Q: 4- Assume the two operators 2 and A are Hermitian. What can you say about a ) ΩΛ b) ΩΛ+ ΛΩ c) [2, A]

A: In Quantum mechanics an operator Ω is said to Hermitian operator if it obeys the following equation.…

Q: Normalize (to 1) the wavefunction e–ax in the range 0 ≤ x ≤ ∞, with a > 0.

A: Given: The wave function is as follows,

Q: What is the magnitude of the angular momentum of an SF6 molecule when it is rotating with its…

Q: 8.11a Confirm that the operator i = (h/i)d/dø, where ø is an angle, is hermitian.

Q: The rotation of a molecule can be represented by the motion of a particle moving over the surface of…

A: Value of angular momentum quantum no, l = 1 Calculation of angular momentum, L: where h/2Π is ħ…

Q: By considering the integral ∫02π ψ*ml ψml dϕ, where ml≠m'l, confirm that wavefunctions for a…

A: The expression for the wave function of a particle in a ring is as follows,

Q: c) What is the ground state energy and wave function of the system, and how can they be interpreted?…

Q: 1/x be normalized

Q: The wavefunction of one of the d orbitals is proportional to sin2θ sin 2ϕ. At what angles does it…

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

Q: Normalize the wave function ψ= A sin (nπ/a x) by finding the value of the constant A when the…

A: Normalization is the scaling of wave functions so that all the probabilities add to 1.

Q: Consider a particle in the following 1D box. The potential in this box has the form: 1 2. V = kx² 2…

Q: (iii) Show that the wave function of the particle in the potential well is NA X w.(x) = C sin n =…

Q: Functions of the form sin(nπx/L), where n = 1, 2, 3 …, are wavefunctions in a region of length L…

A: The wavefunction is given as,ψ = sin nπxLFor n=1, ψ1 = sin πxLFor n=2, ψ1 = sin 2πxL

Q: P7D.8* A particle is confined to move in a one-dimensional box of length L. If the particle is…

A: a.

Q: 2. Which of the following wavefunctions are eigenfunctions d? of the operator dx² For those that are…

Q: 3. Plot the eigenstate and particle probability for a particle in a box, with infinite height walls,…

Q: 2. Which of the following wavefunctions are eigenfunctions of the momentum operator? For those that…

A: Eigen function of an oparetor are those which on applying the oparator we get back the function…

Q: 8. Do the linear momentum operator px and angular momentum operator Lx commute. Can the velocity in…

Q: For the same system as in Exercise E7C.3(a) (Functions of the form sin(nπx/L), where n = 1, 2, 3 …,…

Q: What is the magnitude of the angular momentum of a CH4 molecule when it is rotating with its minimum…

A: Known details, The minimum energy to rotate = 2.11×10–22J Moment of Inertia is 5.27 × 10-47 kg m2

Q: Where are the nodes in the wavefunction for a particle confined to a box with 0 < x < a and n=3?

A: Wave function for a particle in a box with 0 < x < a and n=3 No of nodes = to be determined.…

Q: 4. A quantum simple harmonic oscillator can be treated as a particle of mass m attached to a spring…

A: Concept: Energy of quantum simple hormonic oscillator: E = (n+1/2)hv Where E = energy n =…

Q: Consider the three spherical harmonics (a) Y0,0, (b) Y2,–1, and (c) Y3,+3. (a) For each spherical…

Q: What is the average position of a harmonic oscillator with n = 1? (Hint: Your knowledge of odd and…

A: The answer is given as follows

Q: Identify the normalized wavefunction for a particle rotating about the surface of a sphere with a…

A: Given : Spherical surface and spherical particles. To find : Normalized wave function. Solution :…

Q: P7F.9 In this problem you will establish the commutation relations, given in eqn 7E. 14, between the…

Q: а. Is b.2s с. 2р d. 3d е. 5f How many angular and radial nodes exist for the wavefunctions described…

A: Given orbitals are : a). 1s b). 2s c). 2p d). 3d e). 5f (i). Orbital angular momentum of an…

Q: Without evaluating any integrals, state the value of the expectation value of x for a particle in a…

A: The probability density, ψ2, is symmetrical about x=l2. Therefore, it can be stated that probability…

Q: The operator (x+d/dx) has the eigen value α. Determine the corresponding wave function

A: If we let the eigen function is f(x) and eigen operator is ( x +d/dx ) having eigen value α, then we…

Q: In the space below, write the wave function W, for a one-dimensional quantum harmonic oscillator in…

Q: Consider a particle of mass m confined to a one-dimensional box of length L and in a state with…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider a single particle with rest mass m residing in a one-dimensional space, x. = o for x a,…

Q: Imagine a particle free to move in the x direction. Which of the following wavefunctions would be…

A: A wave function is used to describe a state of the particle. It contains all the dynamic…

Concept explainers

Quantum Chemistry

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.

Question

4.
Given these operators A=d/dx and B=x², can you measure the expectation
values of the corresponding observables to infinite precision simultaneously?

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Introduction and Principles 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

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?
Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?
What is the degeneracy of an h subshell? An n subshell?
8. Do the linear momentum operator px and angular momentum operator Lx commute. Can the velocity in the x direction (vx) and angular momentum in the x direction (Lx) be measured simultaneously to an arbitrary precision?
The operator (x+d/dx) has the eigen value α. Determine the corresponding wave function
Consider the three spherical harmonics (a) Y0,0, (b) Y2,–1, and (c) Y3,+3. (a) For each spherical harmonic, substitute the explicit form of the function taken from Table 7F.1 into the left-hand side of eqn 7F.8 (the Schrödinger equation for a particle on a sphere) and confirm that the function is a solution of the equation; give the corresponding eigenvalue (the energy) and show that it agrees with eqn 7F.10. (b) Likewise, show that each spherical harmonic is an eigenfunction of lˆz = (ℏ/i)(d/dϕ) and give the eigenvalue in each case.
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.
Without evaluating any integrals, state the value of the expectation value of x for a particle in a box of length L for the case where the wavefunction has n = 2. Explain how you arrived at your answer.
Show whether the function V (0) = sin 0; 0 = 0- 2T satisfies the %3D normalization condition. If not find the normalization factor N so that V (0) = N sin 0 will satisfy the condition V² d0 = 1
For the system described in Exercise E7C.8(a), evaluate the expectation value of the angular momentum represented by the operator(ħ/i)d/dϕ for the case ml = +1, and then for the general case of integer ml.
For a particle in a box of length L and in the state with n = 5, at what positions is the probability density a maximum? At what positions is it a minimum?