Find the fourier transform of f(x) defined by f(x) = { = ( and hence evaluate +∞ sin pacos pl du |x|

Q: B/Express f(x) = cos wx, -1 < x < π, as a Fourier series. Hence prove that 2w π(W² - 1²) cot wπ = +…

A: Given, Function of x is f(x) =cosωx

Q: The wave function of a particle is psi(x)=Ae-bx for x&gt;0 and psi(x)=Aebx for x&lt;0. Find the…

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Q: Find the expected ualue of the Harmonic oscillator function Un lx) =Nexp ( *z) Hn Lx)

A: it is required to find the expected value of the given harmonic oscillator function. Here the given…

Q: What is y(x) (i.e., y as a function of x) given that dy dx where you are given the boundary…

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Q: Find the Fourier transform of e=jt

A: Given that:f(t)=e-jtTo determine the Fourier transformation of f(t)

Q: The normalized wave function for a state is given by (r) = (z+ ix)f(r). a) Describe the angular…

A: The normalized wave function for a state is given by

Q: Find the Z Transform for the following function: f(t)=e^(-ct) cos⁡(2πt/3)u(t)

A: To find the Z-transform of the given function, we can first write the function in terms of the…

Q: (1) Working with Y,"(0,4) show that YS (0, 4) and Y}(0,$) are each normalized and that these two…

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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: Let E(r) : Calculate the line integral | E(r) - dr along the path a bc in the following two straight…

A: Let's solve the problem in Cartesian coordinate system. Given

Q: Let V = 6+ j8 and I = -(2 + j3). (a) Express V and I in phasor form, and find (b) VI, (c) VI*, (d)…

A: (a) Phasor form of V is,

Q: By considering the integral ∫02π cosmlϕ cosm'lϕ dϕ, where ml≠m'l ,confirm that the wavefunctions…

A: Normalize the wavefunction…

Q: Find the Fourier series of f(x) on

A: Given function: f(x)=-π   x∈(-1,0),π     x∈(0,1).

Q: ), -G. ), a.) Total differentials: U(V,T) dU - C,dT + RydV S(V,T) ds ar + dv H(P,T) S(P,T) dH - C,dT…

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Q: The Fourier transform of a function f (x) is defined as: f (w) = L dx f (ω) -. f (x)e-iwx Similarly,…

A: Given,  Fourier transform formula and inverse Fourier transform formula  And the function f(x) .

Q: Find the Fourier transform of rect(t/4). (a) sinc(w) (b) sinc(w) (c) sinc(2w) (d) 2 sinc(2w)

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Q: If f(x) is a function with period 2L = 4 given on the interval (−2, 2) with (in the picture) (a)…

A: Given: f(x)=2+x,    -2&lt;x&lt;02-x,       0&lt;x&lt;2 Calculation: First we will calculate…

Q: Ex4@Express w = (x-1) ay in the cylindrical coordinates (b) transform F = P cosa ap in the Cartizian…

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Q: Evaluate the equation of continuity of plane wave function Exp i (kx-wt).

A: Given, Plane wave function,ψ=eikx-wt

Q: Prove that the expression e*/(1+ e*)² is an even function of x.

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Q: Find the Fourier Series corresponding to the f(x) define over interval (-2,2) as follows f(x) = 2…

A: The function fx is defined over the interval -2,2 Now, fx=2, -2≤x≤0x,     0≤x≤2  We know, Fourier…

Q: The eigenvalues a

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Q: Given a function : y(t) = A sin(kx-wt) Prove that: d^2 y / dt^2 = - w^2 y(t) Where A, k, x, w are…

A: Given function is, yt=Asinkx-ωt

Q: Consider the function: z = ( ₁ ) ² Z where x = 13.36 ± 0.03 and, y = 6.27 ± 0.05 are two independent…

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Q: Show that the spherical harmonics Y2,2(θ,φ)= ((15/32π)^1/2)*sin(2θ)*e^∓2iφ and Y3,3(θ,φ)=…

A: Correction Y22(θ,φ)=1532πsin2θ×e±i2φY33(θ,φ)=3564πsin3θ×e±i3φ

Q: If the real part ofa complex analytic function f(z) is given as, u (x, y)= e*" sin(x' -y'), then…

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Q: Calculate the divergences of cach of the following vectors: (a) v = 3k (b) ở = r (c) v = (4xz + y²)…

A: Since you have posted multiple questions, according to company policy we will answer only the 1st…

Q: |jm) is an eigenstate of £2, then its eigenvalue is j(j+1)ħ², Z True False

A: False.   If |j, m⟩ is an eigenstate of the operator corresponding to the square of the orbital…

Q: Legrende polynomials The amplitude of a stray wave is defined by: SO) =x(21+ 1) exp lô] sen ô, P(cos…

A: We have to use property of Legendre polynomial.