What is the value of the commutator [Px , âxª ].

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

A:

Q: Calculate the expectation values of px and px2 for a particle in the state with n = 2 in a…

A: Where, H is the Planck’s constant The wave function for n = 2 in a square well potential is given by…

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

A: The calculation for magnitude of orbital angular momentum when l =2 is shown below,

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: Determine the density of a proton. For a sphere V = () Tr³. 3

A: Given :-  Mass of proton = 1.7 × 10-24 g  Radius of proton = 1.0 × 10-13 cm  To determine :-…

Q: Which of the following functions can be normalized (in all cases the range for x is from x = −∞ to…

A: Given:  Range for x is from -infinity to +infinity. (i) sin(ax) Substitute x= +infinity and…

Q: If we have two operators Ậ = x and Ê = d/dx and a function f(x) = x². Clearly indicate if these two…

A: If two operator commute then AB=BA,where A,B are two operator.

Q: The operation S5 is equal to O1 (perpindicular) A True B) False

A: The improper axis of symmetry assigns a fixed number of rotations for a given molecule. For example:…

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: For a particle in a rectangular box with sides of length L1 = L and L2 = 2L, find a state that is…

A: Degenerate state is that when two or more than two states of quantum system gives same value of…

Q: can the function x2e-ax^2 be normalized in the range of -inf to inf, and if so what is the…

A: A wavefunction is normalized if:

Q: Calculate the linear momentum of a pickup truck that has a mass of 945 kg and is traveling eastward…

A:

Q: For a particle in a rectangular box with sides of length L1 = L and L2 = 2L, find a state that is…

A: Given information, Rectangular box with sides of length L1 = L and L2 = 2L

Q: The commutator of [LxLy, Lz] is equal to

A:

Q: If two functions f (x ) and g (x ) are both eigenfunctions of some hermitian operator, what does it…

A: Eigenfunctions are the functions which contains information about the state of the system and which…

Q: R(x)=x2+9x+8/x+1 What is the equation of the vertical​ asymptote(s) of R(x)​?

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Q: Define, justify, and provide examples of zero-point energy.

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Q: Q: What are the eigenfunctions and eigenvalues of the operator d/dx ? 2 - * 3 - sin2x

A: Eigen function does not have an independent existence. It exsists only with operator and after the…

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: Calculate the Qexp of the outlying result in the data set: 7.68, 5.63, 5.89, 5.28, 5.42, 5.47, 5.06,…

A: Steps to be followed (1) Arrange in increasing order of data set     5.06, 5.28, 5.42, 5.47, 5.63,…

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

A:

Q: 13) Evaluate (p,x) for W1 of a particle-in-a-box.

A: We have to find Px average.

Q: Q6: Quantum chemistry. Please explain as detail as possible

A: When an operator operates on a function produces a constant times the function, known as Eigen value…

Q: Given the following values of AHm,ASîxn, and T, determine ASuniv-

A: ∆G=∆H-T∆S   ∆G= change in Gibbs free energy ∆H=change in enthalapy T=Temperature in Kelvin ∆S=change…

Q: Say whether the one-dimensional kinetic energy operator (at x) is Hermitic.

A:

Q: Draw scale vector diagrams to represent the states (i) l = 1, ml = +1, (ii) l = 2, ml = 0.

A: The vector  diagrams to represent the states (i) l = 1, ml = +1 has to be given, i) The vector…

Q: Which of the following expression/s are not equal to the commutator [x, px³]? (Select all that…

A:

Q: Do the kinetic energy operator and momentum operator commute once they are applied on f(x) =AX?

A:

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: Q.3 (a) is d/dx a linear operator (b) Is √ a linear operator

A: Linear operator are those for which following equality is trueo^fx+gx=o^fx+o^ gxwhere fx and gx are…

Q: Evaluate the following commutators d @[4] (a) x, dx d (b) x, [x [*] dy d (c) dx - x₂ d dx + x

A:

Q: Evaluate the linear momentum and kinetic energy of a free electron described by the wavefunction…

A: In a matter wave, the possibility of finding an electron is called wave function. Basically, wave…

Q: For a particle in a two-dimensional square box of length L, if the particle is in the state w2,3 (x,…

A: Wavefunction of a particle in 2D is given by

Q: 09) What is the degree of the degeneracy of a state You for a particle confined in cubic box A)1 B)…

A:

Q: What are the  Probability Densities?

A: In probability theory, a probability density function, or density of a continuous random variable,…

Q: Derive an expression for the angle between the vector representing angular momentum l with…

A:

Q: How fast would a particle of mass 1.0 g need to travel to have the same linear momentum as a photon…

A: According to De-Broglie wavelength is given by, λ=hmv where h is the Plank's constant, m is the mass…

Q: Linear function y=x Find real life examples of this function

A: The term linear process contributes to two separate but related concepts: A linear function in…

Q: Q18. What is the degeneracy of a state Wizs for a particle confined in cubic box? F) 5 B) 3 C) 4 D)…

A:

Q: m, then what is the uncertainty in its speed?

A: Uncertainty in velocity is equal to 2.9 × 107m.

Q: 6) The relation between the kinetic energy and linear momentum can be expressed by the following…

A: Given Kinetic Energy  Relation between Kinetic Energy and momentum = ?

Q: Find the uncertainty ox in x as a function of the uncertainties ou and oy in u and v for the…

A: Solution.                       Given that (a) x = 1/2(u + v) (b) x = uv^2 (c) x = u^2+v^2

Q: A particle rotating on the surface of a sphere with fixed r has the quantum numbers I = 3 and mj =…

A: The answer is given as follows The orbital angular momentum of the rotating particle is given by the…

Q: Which of these choices is the expectation value of momentum p for a particle in the state n = 5 in a…

A: The reasonable expected value of the result of an experiment is known as its expected value.

Q: Form. Deteímine if Fin d the simpiest the operators are Commuting or noncommuting 1.) and x 1) Ŕ and…

A:

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.