Find the poisson brackets [F,G] for the functions: F = q1 +q2p{ and G = q +2p3

Q: Given that A is Hermitian operator P'rove hat (a) The cigenvalues of operator A are real (b) The…

A: Given A is Hermitian operator.

Q: Shortest Line in 3D Prove that the shortest path between two points in 5. three dimensions is a…

A: The distance between the two points in the three dimensions can be given as follow:

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Q: 2.2. (a) Verify explicitly the invariance of the volume element do of the phase space of a single…

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Q: The divergence and curl of the function f(r, 0, q) = (r* sec 0)e, is ...... (4r^(3 ) sece)er ( [4r)…

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Q: nian is given by H = p2/2m + m[omega]2x2/2. a) Determine the Ehrenfest equations of motion for and…

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Q: Consider two particles of masses m1 and m2. Let m1 be contined to move on a circle of radius a in…

A: the Lagrangian for the system:

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Q: Show that the momentum Operator is a Operator, or (W/P/V); is real number. is Hermition

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Q: Find by the Lagrange multiplier method the largest value of the product of three positive numbers if…

A: Let the three numbers be x, y and z Hence,

Q: F = A +B'C which one of the followings is the representation of function F in terms of SOP form?

A: Steps to write a minimal form of function into canonical form SOP : 1. Find number of variables in…

Q: What does your result for the potential energy U(x=+L) become in the limit a→0?

A: We want to calculate lima→0qQ8πε0alnL+aL-a=qQ8πε0lima→0lnL+aL-aa

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Q: Write the matrices which produce a rotation θ about the x axis, or that rotation combined with a…

A: The matrices which produce a rotation θ about x-axis is given by, A=1000cosθ-sinθ0sinθcosθ

Q: A heavy particle is projected from a point at the foot of a flying plane, inclined at an angle 45°…

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Q: M.Sc Physics QM mean by Pauli's what do you Spin Matrices? Show that Pauli's matrices are spin…

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Q: Consider the following Hermitian matrix 3 1 i 2 1i a) find the eigenvalues find the eigenvectors b)…

A: (a)The eigen values is,

Q: Find the the Gradient of (f(Zy-3))

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Q: find a potential function for F or determine that F is not conservative.  F = xj + yk

A: The given function, F = xj + yk The curl for F to can be determine if the F is conservative or…

Q: Find the Dual of the function below and check if it is self-dual: F4 = (XY + YZ + ZX)

A: SOlution: given that F4 = (XY + YZ + ZX) to verify whether it is self dual.

Q: The eigenvalue of a Hermitian operator is generated to be a complex number integer number complex or…

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Q: Using the condition (3.027) of Lect. 16, prove that the mo- mentum operator p is Hermitian. HINT:…

A: Condition for the operator to be Hermitian, Using the periodic boundary conditions for the functions…

Q: Two mass points of mass m1 and m2 are connected by a string passing through a hole in a smooth table…

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Q: equations satisfies

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Q: Q2: 0 0 The Hamiltonian is represented by the matrix H = u 0 0 1 Where u is positive real number. 1…

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Q: Consider a Lagrangian given by: L(r,i) )= mi2-k?. %3D Here x is the generalized coordinate. Evaluate…

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Q: An anharmonic oscillator has the potential function V = 1/2.(k.x^2) + c.x^4 where c can be…

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Q: Find the modified wavenumber for the operator derived. Plot the real and imaginary parts of K*A vs.…

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Q: If we have two operators A and B possess the same common Eigen function, then prove that the two…

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Q: H.W.: prove that the eigenfunctions , (x) =cos (x) and 3 (x) =cos x) 2a are orthogonal.

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Q: The only possible outcome to measure the observable is one of the eigenvalues of any operator À…

A: Yes, it is true. Eigen values of the operators are the measures to the observable.

Q: Which of the functions below are eigenfunctions of a. sin(3x) b. cos(4x) с. 5х3 d. 1/x е. Зе5x f.…

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Q: How many angular nodes are there for the spherical harmonic Y3,0 and at which values of θ do they…

A: The spherical harmonic are a group of functions used in math and the physical sciences to solve…

Q: Show that the position operator (Ê = x) and the hamiltonian operator (Ĥ : -(n2/2m)d²/dx² + V (x))…

A: Proof for Position operator being hermitian x^ψψ=∫-∞∞xψ*ψdx=∫-∞∞xψ*ψdx=∫-∞∞ψ*xψdx=ψx^ψ

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Q: Show that the following operators are Hermitian, a) Momentum operator b) Hamiltonian operator c) i…

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Q: What do you mean by Harmonic ascillator. Prove that the Hamiltonian tor Harmonic oscillator can be…

A: A harmonic oscillator,  Hamiltonian of harmonic oscillator, H = ?

Q: Show that the operator H = -1/2(d^2/dx^2) is hermitian, assuming that it operates on a Hilbert…

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Q: Q1: 1. The Hamiltonian is represented by the matrix H = @ 0 2 0 Where o is positive real number. 0 2…

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