Find the following commutators by applying the operators to an arbitrary function f(x) [e, x+d²/dx²] [x³ = d/dx, x + d²/dx²]

Q: Which of the following functions f has a removable discontinuity at a? If the discontinuity is…

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Q: Consider a rectangular surface of length L and width W in the xy plane with its center at the…

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Q: By what factors do the operators (xp; + px) and 1/2(xp,+ P,x) differ?

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Q: How is it that I can have b=x in problem 7.48?

A: The total energy of a harmonic oscillator is

Q: Consider the following kets: 2 i |r,) = +|1+ i y Ir2) = [-3i . 2- 2i 4 (ri \r2) and a) compute the…

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Q: A triangle in the xy plane is defined with = (0,0), (0, 2) and corners at (x,y) (4, 2). We want to…

A: The triangle has corners at (x,y)=(0,0), (0,2) and (4,2). We have a function f(x,y) which we need to…

Q: Find the x− and y− components of the vectors A~, B~ , C~ , and D~ . Take A = 10.0, B = 7.00, C =…

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Q: Calculate the commutators [^px, ^x2].

A: Calculate commutator of px with x^2

Q: Find a unit vector normal to the surface xy? + xz = 1 at the point (–1, 1, 1).

A: Given surface-xy2+xz=1P=(-,1,1)

Q: Calculate the following commutators: (a) [P, ² ] (b) [â² , p²]

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Q: b. Verify x a a. Apply the continuity condition(s) to find a relation among the constants to be…

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Q: If A = 2yz i – (x +3y – 2)j+ (x² + z)k, evaluate SS, (V × A)· dS over the surface of intersection of…

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Q: Calculate the commutators [^px2, f(^x

A: Find commutator of px with x^2

Q: x=J_y=K Z=L Let Ġ(J, K, L) = for c, d E R. Find c and d that will make the curl of G (1, zero, 2)…

A: Given, G→x,y,z=<3cx2z,ey+d+xz,xyz>

Q: Evaluate the commutator L,, L, L,- (a) h'L, (b) 0 (c) h'L, (d) h°L.

A: In rotational mechanics, Angular momentum holds a similar place as linear momentum. If Net torque on…

Q: Solve the following system by graphing and verify that your solution satisfies the system. {2x + y…

A: Given : 2x+y=20 x+y=12 In this question we have to find the value of x and y by plotting a graph.

Q: Check if the following operators with the corresponding functions could form an eigen value…

A: Operators form an eigenvalue equation with function, if the function is an eigenvector of the…

Q: Using the method of separation of variables, find the solution of the following equation Pu, Pu = 0…

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Q: Draw a (1 _1 0) plane in a cubic unit cell. Show that all directions that lie on this plane and…

A: Given, (1,1,0) plane with all direction

Q: Calculate the commutators [^px2, ^x2].

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Q: Given V = x2i + y2j + z2k, integrate V · n dσ over the whole surface of the cube of side 1 with four…

A: The divergence theorem is given by, The divergence can be calculated as,

Q: Let B = Z[x] denote the set of all polynomials in x. Show that B is denumerable.

A: B = Zx  = all polynomial with integer coefficient

Q: P-1 Show the given set of function is orthogonal and find the Norm of the function in given set {cos…

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Q: Find Vo (t) for t20 0. 25 H auct-2) E 0-25 H

A: In the given circuit,  Vin = 9 V When the circuit is just closed, that is, t = 0, then the current…

Q: find u(x,y) , v(x,y) where f(z)=u+iv for function f(z)=Z2 e2z

A: Given, A complex function fz=z2e2z

Q: Find the divergence and curl of each of the following vector functions: 1. S = 2. E =

A: Answer 1:

Q: Determine whether F is conservative. If so, find a scalar function f, such that V = Vf a) F = y sin…

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Q: Given ϕ=xy+yz+xzϕ=xy+yz+xz, find gradient ϕ at point (1, 2, 3).

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Q: Consider the matrix representation of Lx, Ly and L₂ for the case l = 1 (see Matrix Representation of…

A: Required to construct the matrix representation.

Q: Let n 1 be an integer, let to to is given by a stationary path of the Lagrangian functional C: L[x]…

A: Given Data:The given Lagrangian is, The generalised coordinates, The generalised velocity, To Prove:…