If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange’s equations, show by direct substitution that L' = L + (dF(q1, ..., qn, t)/dt) also satisfies Lagrange’s equations where F is any arbitrary, but differentiable, function of its arguments.
Q: Suppose that you have three vectors: fi (x) = 1, f2 (x) = x – 1, and f3 (x) = } (x² – 4x + 2), that…
A: We have to Operate by D on f1 Since f1 is a constant function <f1| = |f1>
Q: Two masses and 3 springs. нотот Consider the longitudinal oscillations, i.e., along the axis, of a…
A:
Q: Consider two vector fields X and Y and an arbitrary smooth scalar function f(x). The Lie derivative…
A:
Q: Find the Laplace transforms of the following functions: 1. x2 2. xe6x Subject : DIFFERENTIAL…
A:
Q: Demonstrate that the eigenfunction (Ψ) of the kinetic energy operator of a physical systemTˆ, will…
A: We are given eigen function of kinetic energy operator. We then are given that potential energy…
Q: Consider a block of mass m on the end of a massless spring of spring constant k and equilibrium…
A: Since you have posted a question that has more than three subparts, we will solve the first three…
Q: Let T:V to V be linear with finite dimV=n, if f(x)=(-1)^n (x-λ_1)^α_1...(x-λ_r)^α_r Let W be a…
A: Its given That f(x)=(-1)n (x-λ1)α1...(x-λr)αr
Q: Spherical Tensor and Wigner-Eckart theorem It is claimed that Σ,(-1) S(T) is a scalar operator.…
A: The objective of the question is to verify the claim that the sum of (-1) times S(T) is a scalar…
Q: Consider the following operators defined over L, (R): d = x+ dx d *** Î_ = x dx Show that Î,Î = 2.
A: Commutators of two operators A and B is given by [A, B] = AB - BA
Q: Consider the initial value problem where is a given number. yty + 0.03y³, y(0) = x, Draw a direction…
A: In this question we have to find the critical values. Please give positive feedback if the answer…
Q: () = 1- (器)
A: we can explore the properties of Hermitian operator to prove the following statements. Let the…
Q: Obtain the value of the Lagrange multiplier for the particle above the bowl given by x^2+y^2=az
A: To find the Lagrange multiplier for the particle above the bowl defined by x2+y2=az, we need to set…
Q: Given a particle of mass m in the harmonic oscillator potential starts out in the state mwx (x, 0) =…
A:
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: Divergence theorem. (a) Use the divergence theorem to prove, - -478'(7) (2.1) (b) [Problem 1.64,…
A: b As given, Dr,ε=-14π∇21r2+ε2 By differentiating we get, Dr,ε=-14π ddrddr1r2+ε2=-14π…
Q: Find the Laplace transform of ( 1 + cos2?)
A:
Q: Assume the operators  and B commute with each other, show that a) The matrix representation B in…
A:
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: The Hamiltonian of a system has the form 1 d² 1 · + ²⁄3 x² + √4x² = Ĥo + Y₁X² 2 dx2 2 Ĥ = == Let…
A:
Q: Using the formula for Euler-Lagrange EOM, one can find the Lagrangian and the EOM for a mass sliding…
A: Given data, A particle of mass m is sliding on a frictionless inclined plane.
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: = Ae-**/b* show that, if A is chosen properly, Consider the function 4 (x) 4(x) behaves like a Dirac…
A: Given: The function is ∆(x)=Ae-x2b2. Introduction: As a distribution, the Dirac delta function is a…
Q: (1) Lagrange multiplier is a very useful technique to determine the extremum of a function under…
A:
Q: A wire of the shape of y=ax² is rotating around its vertical axis with an angular velocity wo (see…
A:
Q: (a) Construct 3-dimensional matrix G that representing the action of the operator H. (b) If the…
A:
Q: Solve for y1(t) and y2(t) using Laplace Transforms and the initial values. You may check your work…
A:
Q: (a) Suppose that f(x) and g(x) are two eigenfunctions of an operator 2, with the same eigenvalue q.…
A: Since you have have asked multiple question, we will solve the first question for you. If you want…
Q: Suppose I have an operator Â, and I discover that Â(2²) = 5 sina and Â(sin x) = 5x². (a) Find Â(2²…
A: A^(x2)=5 sin xA^(sin x)=5 x2
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: #1: Find the time depended wave functions V(x, t) = ?
A:
Q: Consider the operator  such that for function f(x) we have: Äf(x)= f(x+a)+ f(x-a). The domain for…
A:
Q: Calculate the reflection coefficient R and the transmission coefficient T of the scattering caused…
A: Answer
Q: Assume the operators Ä and B commute with each other, show that b) The kets |A1), |A2), ... |AN) are…
A:
Q: Sketch f(y) versus y. Show that y is increasing as a function of t for y < 1 and also for y >…
A:
Q: Show explicitly how to construct the L^3 operator. Then determine if the spherical harmonics (Yl,m)…
A:
Q: Claim: For any function † (q,p,t), df Proof: df = dt af {f, H} + (4.62) Ət af af af Ət - %+%*+% = dt…
A:
Q: Construct the ket |S n; +) such that S nS n (h/2)|S n; (1) where n is a unit vector with polar angle…
A: Let k = ℏ/2. Treating the given problem as an eigenvalue problem described by the eigenvalue…
If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange’s equations, show by direct substitution that
L' = L + (dF(q1, ..., qn, t)/dt)
also satisfies Lagrange’s equations where F is any arbitrary, but differentiable, function of its arguments.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
- Consider the following operators on a Hilbert space V³ (C): 0-i 0 ABAR-G , Ly i 0-i , Liz 00 √2 0 i 0 LE √2 010 101 010 What are the corresponding eigenstates of L₂? 10 00 0 0 -1 What are the normalized eigenstates and eigenvalues of L₂ in the L₂ basis?a2 Laplacian operator 72 = ax? ay? T əz2 in spherical polar coordinates is given by az? p² = () 1 a 1 1 a2 r2 sin e ae sin 0-) is an eigenfunction of the Laplacian operator and find the +- r2 sin 0 a0 r2 ar ar. r2 sin? 0 a20 sin 0 sin o Show that function r2 corresponding eigenvalue.My system is a pendulum attached to moving horizontal mass m_1 and the pendulum m_2 that is shifted by X_o from origin. I have the lagrangian of my system what would be my equations of motions in terms of small angle approximation and what’s is their frequency?
- Find the separable solution of Laplace's equation (r, 0) = f(r)g(0), where r and are polar coordinates, describing a planar two-dimensional potential flow past a wedge (see the figure below). 00 Show that in this solution the flow speed * = Apa-1 2π where A is an arbitrary constant, a = and the angle < 0o < 27 is defined in the 1 00 figure above.Provide a written answerlog z = log r + i is holomorphic in the region r>0 and - < 0 <. 10. Show that where z = re¹ with - < 0 < where is the Laplacian Ә əz əz A = 4 əz əz dx² 8² dy² 11. Use Exercise 10 to prove that if f is bolomorphic in the open set , then the real and imaginary parts of f are harmonic; that is, their Laplacian is zero.
- Consider the polar-coordinate stream function ψ = Br1/2sin(1.2 θ), with B equal, for convenience, to 1.0 ft0.8/s.(a) Plot the streamline ψ = 0 in the upper half plane.(b) Plot the streamline ψ = 1.0 and interpret the fl owpattern. (c) Find the locus of points above ψ = 0 for whichthe resultant velocity = 1.2 ft/s.Find a potential function for F or determine that F is not conservative. (If F is not conservative, enter NOT CONSERVATIVE.) F = (2xy + 3, x2 – 22, -2y)