7. Expectation value of an arbitrary operator B satisfies the following equation of motion d a B [(B) = ( ³ ) + ([A, B]) . dt at h
Q: 1. Show that the function (x) = 6x³ is an eigenfunction of the operator А = X What is the…
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Q: 5. If V(x) = kx¹, what is the average value of kinetic energy 4 Ans: (2m)? Express by (V).
A: By using virial theorem we can calculate question (5) easily. As per bartleby's guidelines i solve…
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Q: Q2. If you are given the following operator 03, acts on function of position 4(x). as: O34(x) = v(x)…
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Q: Suppose that you have the functional J (a) = S². ƒ {y(a, x), y' (a, x); x}dx where y (a, x) = 3x – a…
A: Given, Jα=∫-π2π2fyα,x,y'α,x;xdxyα,x=3x-αcos2xTherefore,y'α,x=3+αsin2x
Q: 16. If A and B are Hermitian operators and [A, B] = o, then they share 17. It is common to label…
A: If A and B are Hermitian operators and [A, B] = 0, then they share a common set of eigenvectors. To…
Q: c): A particle of mass m moves in a three-dimensional box of sides a, b, c. If the potential is zero…
A: Given a particle of mass in a three dimensional infinite depth box of sides a, b and c, where…
Q: 10. An eigenfunction of the operator d²ldx² is sinnx, where n = 1, 2, 3, ... Find the corresponding…
A: Given: The operator is A^=d2dx2. Eigenfunction is ψ=sinnx.
Q: c) Corsider the orthonormal basıs {17, 1273, the stote I Y>= l174 e® 27 and the operators and answer…
A: We will do the second part first to get a clear picture of solution
Q: What are the indices (Miller indices) of a plane whose intercepts with three axes are 2,4,2,…
A: The given intercepts are 2,4,2.
Q: 4. Consider a set of orthonormal eigenfunctions 4i of the operator 4 (where 4 = a, 9. ) and the so…
A: Here we have a very important as well as easy question. The trick here is to first check for…
Q: I am am doing problem 5. from Serway and Vuille - 11th edition. I dont understand why they use sin…
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Q: 1. Write the general equation for the spherical harmonic Y,'(0, $) and identify Om($), P;" (cos 0),…
A: 1. The general expression for spherical harmonic is given as: Ylm(θ,ϕ)…
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Q: (b) f(x) = Acos(ax), = d2/dx2, where A and a are constants (c) f(x) = Ae-ax,…
A: By using eigenvalue equation, where for a function ψ the eigenfunction of operator Q^ Q^ψ = λψwhere…
Q: 2. Charging a capacitor through a resistor. The capacitor initially starts with no charge. Refer to…
A: For the R-C network, the value of the resistance is, R=1800Ω, the value of the capacitance is,…
Q: * and p are two operators which satisfy [x, p]=i. The operators X = x cos o +p sin o and Y = - x sin…
A: Given: x,p=i. X=xcosϕ+psinϕ. Y=-xsinϕ+pcosϕ.
Q: Q7 Which of the following are eigen functions of the operator d2/dx2 , find the corresponding eigen…
A: The given functions are: (i) sinx (ii) sin2x (iii) e2x TO DETERMINE: The eigen function and the…
Q: b) Prove that the following operators are Hermitian 1) Z 2) Lx
A: (1) Z is z component of position operator. Since position operator r = (X, Y, Z) is hermitian.…
Q: Two wavefunctions, Y, and 42, are each eigenfunctions of the operator Ô, with eigenvalues wi and wz.…
A: Wavefunction The wavefunction of a particle is a mathematical function that encodes all the…
Q: Which function is an eigenfunction to the operator = k ax a.) f(x) = sin(ax) b.) c.) d.) e.) f(x)…
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Q: a. Use the Cartesian representation L₂ = 1/(x2-17 - 1²/²7) y i ду дх to show that (x + iy)m is an…
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Q: 5. Identify which of the following functions are eigen functions of the operator d/dx: а. е b. cos…
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Q: Given that, in free space E = Em sin (wt-Bz) ây. Find D, and Ja. Then show that . (V × D)=0.
A: Let E denotes the electric field vector, E0 denotes the electric field magnitude, ω denotes the…
Q: 1. Consider the matrix operator A = 2. 1. 4 2. a. Show that 3 is one of its eigenvalues, b. Find the…
A: Given: A=-2-42-212425
Q: 11. Evaluate (r), the expectation value of r for Y,s (assume that the operator f is defined as…
A: For hydrogen atom the ground state wavefunction is, ψ1s=e-ra0πa03/2 (1)where a0=0.0529nm…
Q: A particle is described by the following function: A Y = , for 1 < x < 4 (x+1)(x²+9)²' a. Find the…
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Q: d² Let  = Consider the orthonormal basis: dx² | 1) = $1(x) = √√sin (x) and 2 [2) = ₂(x) = sin (2x).…
A: Given that |1> = ϕ1(x) = 2LsinπxL.................(1)|2> = ϕ2(x) =…
Q: Show that the momentum operator in the position representation is given in the form: er d p=-ih-+…
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Q: 0 A physical system is described by a two-dimensional vector space with Hamiltonian operator Ĥ given…
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