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

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: Suppose that particle in two-dimensional (2D) box a a x; 30 V(xy) = x(а — х) у(b-у) (a³b5)i] Show…

A: We have the following two  points from the question: The particle is in a 2D box The wave function…

Q: describe in words how R^2 and the volume function individually contribute to the radial probability…

A: The radial probability density is the square of the wave function [R2nl(r)] and the volume of the…

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: 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: What is the degeneracy of a molecule rotating with J = 4?

A: Degeneracy of energy levels- Simple meaning of degeneracy of energy levels is energy levels with…

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

A: Determine magnitude of the angular momentum of an SF6 molecule:

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: 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: List all the possible theoretical values of I if n=5. А. 1 В. З C. 4 D. 2 Е. О F. 5 G. 6 Rationale:

A: l can have any values 0 to n-1.

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

A:

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: Confirm that the kinetic energy operator, −(ħ2/2m)d2/dx2, is hermitian.

A:

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: using the classicial definition of kinetic energy K=1/2mv^2 and the quantum mechanical definition of…

A: From classical definition of kinetic energy and momentum, the relation between them is given as,…

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: a) The physical interpretation of the wavefunction and the fact that it is a solution of the…

A:

Q: State whether each of the functions (a) to (d) is quadratically integrable.(a and b are positive…

A: This problem makes use of the following test for quadratic integrability. For a function, if: On…

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

A:

Q: Construct the 3 triplet and 1 singlet wavefunction for the Li+ (1s)' (2s)!

A: Due to technical error ,unable to provide you the solution. Please resubmit the question once again

Q: Calculate the molar heat capacity of a monatomic non-metallic solid at 298 K which is characterized…

A: The heat capacity guides the amount of heat required to increase the temperature of a substance by…

Q: Which of these choices is the expectation value of momentum squared p2 for a particle in the state n…

A: The expectation value p2 for a particle in the state n in a square well potential is given by

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

A:

Q: For a system rotating in three dimensions. what is the degeneracy of the level with I=4? What are…

A: Magnetic quantum number It specifies the orientation in space of an orbital. s-subshell has one…

Q: (a) If  = 3x? and B = , then show that  and ß donot commute with respect to the dx function f(x) =…

A: Commutator of A & B is generally represented as :         The operation is possible with taking…

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

A: We have to find Px average.

Q: What is the relation between the Debye length and the zeta potential?

A: Debye length is a measure of the charge carriers net electrostatic effect in the solution.In other…

Q: For a system consisting of three particles in 3D, on what variables does the time-independent wave…

A:

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

A:

Q: A certain system with a wavefunction v is the linear combination: where yl and y2 are energy…

A: We have to calculate the probability that the system will be observed to be E1 and E2:

Q: Evaluate the linear momentum and kinetic energy of a free proton described by the wavefunction e−ikx…

A: Wavefunction = e-ikx Where, k = 5 nm-1

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

A:

Q: Given the matrix representation for the operator Sy (C ). Find the eigenvalues and eigenvectors of…

A:

Q: Calculate the molar heat capacity of a monatomic non-metallic solid at 500 K which is characterized…

A: The molar heat capacity is determined using the following equation Einstein equation…

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: 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: For a particle in a two-dimensional box with sides of equal lengths, draw rough sketches of contours…

A: The state of any particle can be defined by the wave function. The probability of finding an…

Q: Describe and justify the Born interpretation of the wavefunction.

A: The Born interpretation of the wavefunction has to be described below.

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

A: We are given commutator [px^ , x^4]  We've to calculate it's value.

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

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

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.