se the wave function is an eigen function of A=a/ax+a/ay W3lx,y)=e-2x2+y 1O w{ x,y) =sin2xcos 5x . O Wz(x,y)=e-i(x +y) .III O

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A: solution to the given question is like this;first find eigen values and check they are real distinct…

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A:

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Q: The eigenfunctions for the BVP: 0 XX (0, t)%3D0 (1, t) 0,

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Q: Use the Fourier transform to solve the BVP Ugr + Uyy = 0, -∞ 0 u (x, 0) = f (x) lim u (x, y) = 0,…

A: Given that, Uxx + Uyy = 0, −∞ < x < ∞,  y > 0, U(x, 0) = g(x)lim U(x, y) = 0 , |x|→∞, y→∞…

Q: What are the Eigenvalues of the system below dx | dt dy dt = 2x + y -X

A: The differential equations are:To Do:We have to determine the eigenvalues of the system.

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Q: Show that Tr[-APN] ≥ CL-2N, by considering the eigenvalues of the Stokes' operator -A.

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Q: Using the attached theorms, Solve dx/dt =4x+y , dy/dt=-2x+2y

A: Step 1: Step 2: Step 3:

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Q: Consider the function ƒ = kre¯¹¹²ª sin0 e¯ where k is constant and the operator 2² 20² 2 = -ħ² +…

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Q: Find the eigenvalues and eigenspaces for (a) Each of the Pauli operators X, Y, Z;

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 4) Which of the following functions are eigen functions of the operator dx ? Show your proof. a) eax…

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Q: 6. Show the validity of the following the 2-D discrete Fourier transform pairs: (а) б(х — Хо, у —…

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Q: 7. Find the eigenvalues and (a) Each of the Pauli op (b) the operator Se=

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Q: 2.- a) find eigenvalue/eigenvalues and the corresponding eigenvector/eigenvectors of A. b) consider…

A: Given system of differential equationx′=−x+5yy′=−yWhich can be written as in matrix…

Q: The eigenfunctions for the IBVP Ut =u x +t; 00 X, u,(0, t) = 0 u,(1, t)= 0 u(x, 0)= cos x %3D u,(x,…

A: We are given utt=uxx+t; 0<x<1, t>0ux(0,t)=0ux(1,t)=0u(x,0)=cosxut(x,0)=x

Q: a) Let T(x), n = 1,2,3, ... are the eigenfunctions of the Sturm-Liouville problem; x³y" + 2x²y' + λy…

A: a) The  solution for the Slurm-Liouville problem is explained below, but the values of a, C, and D…

Q: La transformada de Fourier de x(t) = e2t * u(- t)

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Q: ) Consider again the ODE introduced in point (a) and describing the motion of the pendulum me0=-mg…

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Q: Show that the function, f(y) = (16y4-48y2 + 12) exp (-y2/2) is an eigenfunction of the operator, B…

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Q: 2. Show that the wavefunction (eigenfunction) of a state |a) can be expressed in position basis as…

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Q: Find invertible representation of Y, = 0.9Y;-1 + e; + 0.5e;-1

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Q: Define TE L(C²) by T(w, z) = (-z, w). Find the generalized eigenspaces corresponding to the distinct…

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Q: The eigenfunctions for the IBVP 00 U(0, t) = 0 u,(1, t)=0 u(x, 0)= cos x u(x, 0)= x are 2n +1 = sin…

A: Given : IBVPutt=uxx+t ;        0&lt;x&lt;1,    t&gt;0ux0,t= 0ux1,t= 0ux,0=cos xutx,0=x To find : the…

Q: (ii) Prove that the product of matrices cos²0 Icos@sin0 cos@sin@] sin?e cos²p B = lcosøsing…

A: Given the matrix is A=cos2θcosθsinθcosθsinθsin2θB=cos2φcosφsinφcosφsinφsin2φ