Reverse the Legendre transformation to derive the properties of L(qi, q˙i, t) from H(qi, pi, t), treating the q˙i as independent quantities, and show that it leads to the Lagrangian equations of motion.

Q: Show that Pz is the constant of motion for a particle moving in the central field with Poisson…

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Q: For each of the following tensors determine its type (covariant, contravariant), its range and say…

A: It is possible for you to look at this specific instance of a contravariant tensor, which has the…

Q: Q = (x² + p²) (x + p) — iħx + iħp.

A: To determine whether the operator Q corresponds to an observable, we need to check if it satisfies…

Q: Consider two vector fields X and Y and an arbitrary smooth scalar function f(x). The Lie derivative…

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Q: After achieving the space X missions, the space shuttle carry the crewed capsule back to earth. Well…

A: (a)

Q: masses m and 2m are connected by a light inextensible string which passes over a pulley of mass 2m…

A: Given data: The masses are, m1=m m2=2m The mass of pulley is M=2m. The radius of pulley is r=a.

Q: Considering the objects m_1 and m_2 hanging from a frictionless pulley with a mass M and radius R,…

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Q: e.m

A: Given data, Mass of each ball = m Spring constant of both springs = k1 and k2

Q: Show that the equation of motion of a particle of mass m with spatial coordinate r and velocity v in…

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Q: Consider the Lagrangian function 1 L = m (x² + j² + ż²) + 16ý sin (x – t), where m is a positive…

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Q: If A =2yzi-x^2 yj + xz(^2)k, B = 3xi +4zj -xyk and ∅= xyz, find (Ax ∇)(B.∅)

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Q: Q.3) The motion of a particle of mass m undergoing constant acceleration a in one dimension is…

A: We use both the methods given in the question to show that the given transformation is canonical.

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

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Q: with r > 0 and ~+2. Consider the following line element: ds* = dr2 + tanh(r) do, (a) Compute the…

A: Part a:- The Christoffel symbols (also known as connection coefficients) can be calculated for the…

Q: A projectile started from O at an elevation α. After t seconds its position appeared to have an…

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Q: Suppose that A,, is a covector field, and consider the object Fμv=O₁ Av - O₂ A₁. (a) Show explicitly…

A: The objective of the question is to prove that the definition F = ∇A - ∇A, which uses the covariant…

Q: Consider the similarity transform of a matrix a to A’ given A’ = S-1AS. You need to prove | A n | =…

A: as A'=S-1AStherefore1.    (A')n=S-1ASS-1ASS-1AS...........S-1AS       where the term in square…

Q: (v²) = √ √/²8 (vx) dvx g (v) = √√ vf (v) dv (1²) = √ √²2 ƒ (v) dv

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Q: In terms of the î and p operators, calculate the following commutation relations. You can assume…

A: Use the commutation formula of [x,p] and related properties,

Q: Anisotropic Oscillator (Anisotropic Oscillator) is a kind Consider a rational two-dimensional…

A: Given,Considering two dimentional anistropic oscillator in x and y direction.For a two dimentional…

Q: Consider a charged scalar particle of mass m with charge q and describe a suitable modification of…

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Q: A wire of the shape of y=ax² is rotating around its vertical axis with an angular velocity wo (see…

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Q: Consider the function p(1,2) =(1s(1) 35(2) + 3s(1) 1s(2)] ta(1) B(2) + B(1) a(2)] Which of the…

A: Introduction: Particles whose wave functions are symmetric under particle interchange have integral…

Q: What is vector Poisson equation? Give its physical significance.

A: The physical significance  of poisson  equation  Is that it gives  amount of electric  vector…

Q: e scalar and vector potential given by A → A + ∇ψ(r, t) φ → φ − (1/c) (∂ψ/∂t) , where ψ is arbitrary…

A: When the gauge transformation is performed we have  A=A+∇ψ(r,t)ϕ=ϕ-1c∂ψ∂t The Lagrangian of the…

Q: U = PV P = AT2 Find F0(U,V,N) and F1(U,V,N) After that use, Gibbs-Duhem to prove dF2=0 and…

A: We need to express F0 and F1 in terms of the extensive variables (U, V, and N) and the intensive…

Q: Solve this problem

A: To calculate the electromagnetic momentum (PEM) for the given case, where the charge density for…

Q: Generate all the Legendre functions from the relation U = U(S, V, n) of an open one-phase system and…

A: Given: The functional form of internal energy U=U(S,V,n)

Q: Consider the spherical pendulum, which consists of a mass m suspended by a string from the ceiling.…

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Q: Consider a point particle of mass m moving in one dimension with potential V(x). The system is…

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Q: Consider a Maxwellian distribution: f(v) = (a) Find (vx) (b) Find (v²) (c) Find (mv²/2) 1 (PEA VE) 1…

A: We have given Maxwell's distribution

Q: Consider a Lagrangian given by: L(r,i) )= mi2-k?. %3D Here x is the generalized coordinate. Evaluate…

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Q: The motion of a particle of mass m in a constant magnetic field directed along the 2 axis can be…

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Q: Solve this problem

A: To calculate the electromagnetic momentum PEM for the given scenario, where q1 is stationary and q2…

Q: Claim: For any function † (q,p,t), df Proof: df = dt af {f, H} + (4.62) Ət af af af Ət - %+%*+% = dt…

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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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