(a)Define laplace transform of a function f(t) and its inverse. Is inverse unique ? (b) Obtain a formula for laplace transform of nth derivative of a function f(t).

Q: Using the Laplace transform to find the current i(t) in the circuit: vit) Assume zero initial…

A: R=2 ΩL=1 HC=0.1 Fv=255 sin t  V             0< t<2π   = 0…

Q: Verify that the operator in momentum representation is given by use the methods shown in class by…

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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: (a) Define fourier transform of a function f (t) use it to obtain Fourier integral represtation of…

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Q: Normalize the wave function e-(2r/b) sin sin over the interval 0 ≤r <∞,0 ≤ 0 ≤ T, 0≤ ≤ 2π. The…

A: To normalize wave function, we integrate the square of wave function. So when we integrate over…

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: Start with the definition of H, and use a Maxwell relation to derive the following equation:

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Q: A and B So is normalized. A $(x)-[Bx 6x for 05x59 for a5x56

A: Since you have have asked multiple question, we will solve the first question for you. If you want…

Q: Find the transition matrix ABCD for a laser resonator consisting of a concave-plane mirror and a…

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Q: Obtain the required relation please

A: Using the concept of relative velocity in x-axis;

Q: x 0; what is the energy E? (answer in Vo) 0, 3. For a potential step V(x) = { 1 Ans: Vo, if the…

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Q: Derive the quantun mechanical expression for the s-wave cross section for scattering from a hard…

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Q: *Chapter 21, Problem 029 GO In the figure particles 2 and 4, of charge -e, are fixed in place on a y…

A: Solution:   Given Values,   y2=-8.72 cmy4=4.36 cmx1=-8.72 cmx3=8.72 cm

Q: The point P(25, 9) lies on the curve y = secant line PQ for the following values of x. VI + 4. If Q…

A: slope is given by, m = ∆y∆x a) if x = 25.1 y=f(25.1) =9.0099 slope  = 9.009-9.00025.1-25m = 0.09 b)…

Q: Find Laplace transform of the function t2 Sint.

A: We haveLt2 sin 2t=-12d2ds2Lsin 2tLt2 sin2t=dds×dds2s2+4=dds-4ss2+42=s2+42-4+4s.2s2+4×2ss2+44Lt2 sin…

Q: Consider a uniform source of neutrons in a diffusive, non-absorbing medium located between two…

A: Given: Uniform source in a diffusive, non-absorbing medium Two concentric sphere of radii a and b…

Q: a b с Consider electromagnetic waves for which the relation γεμ /w² - w² C between wave number k and…

A: You have provided a question with multiple parts. So according to our guidelines, I can only solve…

Q: Let Z = 0X0|- |1X1| in the Hilbert space C². Calculate HZH |0) and HZH|1), where H is the Hadamard…

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Q: The translation operator for a finite spatial displacement is given in several dimensions by T(l) =…

A: Solution: Given Operator: T^(l)=exp-2πiplh

Q: Find the Laplace transform of ( 1 + cos2?)

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Q: Ct+CCx = 0. que for any choice of

A: Given as, ct+ccx=0 Fρ=ρ-ρ2

Q: A hollow cylinder moves vertically up and down in water according to the equation y′′ + 6.5 ? = 0.…

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Q: Find the minimum acceleration needed for a maglev train to reach a speed of 430 km/h in 3.0 km, one…

A: Given data: The speed of the maglev train is v=430 km/h. The distance is s=3.0 km. Calculate the…

Q: Consider the two planes (5x+y-z=0) and (x-2y+3z=-1) Argue why the intersection of these two planes…

A: Intersection of two planes:

Q: Obtain a nth derivative formula for Laplace transform of of a function f(t).

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Q: Laplace transform of cos t + 2 t3 + sin(4t) is

A: RecallLf(t)=∫0∞e-stf(t)dtLcosat=s/s2+a2Lsinat=a/s2+a2Ltn=n!/sn+1

Q: Consider a one-dimensional scalar field f(x) = A (2x -) defined for -1 sxs1where x is the gauge…

A: Given: The one-dimensional scalar field is f(x)=A2x-x22 To calculate: The effective measurand  The…

Q: What would happen to the incident wave (x) = Ae¹kx at x < 0 that sees a step potential in the form…

A: a) Incident wave function is, ψx=Aeikx   at       x&lt;0 Potential is, Vx=iΓ Here, i is complex and…

Q: Starting with the equation of motion of a three-dimensional isotropic harmonic ocillator dp. = -kr,…

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Q: Calculate the period of oscillation of ?(x,t) for a particle of mass 1.67 × 10-27 kg in the first…

A: This question can be solved by using quantum mechanical equation.potential well formula

Q: Calculate the reflection coefficient R and the transmission coefficient T of the scattering caused…

A: Answer

Q: Sketch f(y) versus y. Show that y is increasing as a function of t for y &lt; 1 and also for y &gt;…

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Q: Laplace transforms find broad applications in the modelling of oscillators for energy harvesting…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: use Euler’s identity, e^iθ = cos(θ) + (i)sin(θ), prove that sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

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Q: Prove, in explicit steps, that the electric field Ey(x, t) = Egy cos [k (x + ct)] is a solution of…

A: Given, The electric field Eyx,t=E0ycoskx+ct