The action of a system describes all of its possible trajectories in time, and it can be calculated as: Group of answer choices - The time integral of the Hamiltonian - The time derivative of the Hamiltonian - The time derivative of the Lagrangian - The time integral of the Lagrangia

Q: A particle of mass m described by one generalized coordinate q moves under the influence of a…

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Q: Write down the Hamiltonian for a projectile and determine the Hamilton's equations of motion in…

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Q: mass m moves in a plane under the influence of a central force

A: According to the question, ody moves in the central force motion which depends only upon the…

Q: We'll start by using a Gaussian trial function with the variational parameter a, se-ar? trial a. For…

A: Trial function is given , our task is to calculate the E (see in the photo )

Q: 420 for a 2D 21 (;2 + 0 r² ) + Suppose that you have the Lagrangian L system in plane polar…

A: Lagrangian The Lagrangian of a system is a mathematical function that is a function of the…

Q: 2. 1D Ising model Consider the Ising model in 1D with zero external field. The Ising Hamiltonian in…

A: 1. Ground-state energy:The ground state of the 1D Ising model with zero external field has all spins…

Q: Q4: a) Calculate: (uz|A*|u6). b) If the Hamiltonian of harmonic oscillator defined as H = ħw + A*A…

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Q: H = ħwo 3 -i30 0 02 B = bo 7 | (0)) = i 1-i 1+i 1-i 6 D = (e₁] (0)) €₂(0)) (€3] (0)) 0 0 0 2a 2α 0…

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Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…

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Q: Quantization of elastic waves. Let N particles of mass M be connected by a spring of force constant…

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Q: Verify that the Hamiltonian equation H(x, p, t) = T + V = p2/2m + (k/2) (x − v0t)2 leads to the same…

A: The Hamilton’s equations of motion are ∂H∂p=x˙, and ∂H∂x=-p˙ From Newton's second law p˙=mx¨

Q: 3. Consider a pendulum of mass m suspended by a massless spring with unextended length b and spring…

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Q: the motion, and so is the quantity F(x, p, t) = x − pt/m. (a) Compare {H, F} with ∂F ∂t . Prove…

A: Given,F(x,p,t)=x-ptm(a) As we know,dFdt=F,H+∂F∂tFor free particle H=p22m[H, F]=p22m, x-ptm[H,…

Q: Consider a free real scalar field $(x„), where r, = r, y, z for u = 1,2,3 and r4 = ict, satisfying…

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Q: 7-16. The point of support of a simple pendulum of mass m and length bis driven hori- zontally by x…

A: There is a simple pendulum of mass m length b .Horizontal support x = asin(omega.t)

Q: Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m² /C². Vacuum…

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Q: A particle of mass m oscillates in a vertical plane suspended by a massless string that goes through…

A: This is the problem with the simple pendulum with a variable length of the pendulum.  That is  of…

Q: For motion in a plane with the Hamiltonian H = |p|n − a r−n, where p is the vector of the momenta…

A: Given: The Hamiltonian of the motion in a plane is   The operator

Q: The Hamiltonian of consisting of a mass' m less sing of length. a simple pendulum attached' to a I…

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Q: Problem 3 The Lagrangian of a particle in spherical coordinates is given by 1 L(r, 0, 6; 1, 0, 0) =…

A: Step 1:The Lagrangian given for a particle in spherical coordinates is given in question Step 2: The…

Q: Since the Hamiltonian is obtained using a Legendre transform from the Lagrangian, these two…

A: Lagrangian mechanics Hamiltonian mechanics One second order differential equation Two first…

Q: A bead slides on the inner surface of a paraboloid z= C * r^4, as shown in Figure 2. C is a…

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Q: For the motion of a projectile write the Lagrangian and the Hamiltonian functions in polar…

A: The Lagrangian of a system is defined as:L=T-V………(1)where,T is the Kinetic energy.V is the Potential…

Q: 25. (a) The Hamiltonian for a system has the form H 1 = 1/2 ( 72²2 + P²³²₁^²) . Find the equation of…

A: (a) The Hamiltonian for a system has the form H = 1/2 (1/q2+ p2q4). Find the equation of motion for…

Q: Consider a region of space divided by a plane. The potential energy of a particle in region 1 is U₁…

A: Given that a region of space divided by a plane. The potential energy of a particle in region 1 is…

Q: Consider a block and a wedge. The block (mass m) has no friction when it moves on the wedge (mass M)…

A: Given: The mass of the block is m. The mass of the block is M. The angle of inclination is α.…

Q: 2. (a) Formulate the principle of minimum (or stationary) action. You may explain it in your own…

A: 2(a) Principle of minimum action:It is a variational principle that when applied to the action of a…

Q: Find the Hamiltonian and the equation of motion for a mass connected to a horizontal plane A with no…

A: To find the Hamiltonian and the equation of motion for a mass connected to a horizontal plane with…

Q: In the o field theory, the Lagrangian density is 1 Problem 1 -- 4! Find the equation of motion and…

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Q: A material point of mass m moves in space under the influence of an astral field forces, known…

A: A material point of mass m moves in space under the influence of an astral field forces, known…

Q: The free space Lagrangian for a particle moving in 1D is L (x,x, t) = a) Show that pat = SL = ymv b)…

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Q: Question 3 If the Lagrange's function for mechanical system is L = ;k (é² + g²(sin 0)² ) + g cos e.…

A: The Lagrangian is  L=12kθ˙2+12kϕ˙2sin2θ-gcosθ

Q: The transformation Q = λq, p = λP is canonical while the same transformation with t time dilatation,…

A: The given transformation is canonical when, Q=λq and p=λP. The given transformation is not canonical…

Q: Q3: 0 1 The Hamiltonian is represented by the matrix H = B| 1 0 0 %3D 0 2 Where ß is positive real…

A: given: H=β010100002 Where, β is positive real number

Q: Find the equation of motion and the Hamiltonian corresponding to the Lagrangian L * = {{@, 9)² =…

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Q: Given the Hamiltonian H = p²/2m + a · p + V, with a = a(r) and V = the corresponding Lagrangian. If…

A: Here given that, Hamiltonian is H=p22m+a.p+V......................1Legrangian is the Logendre…

Q: Consider a pendulum of length L whose suspension point can move freely on the X axis. 1) Determine…

A: The x and y coordinate of the mass is :  x=X+Lsinθy=-Lcosθ The kinetic energy of the mass is :…

Q: 7-12. A particle of mass m rests on a smooth plane. The plane is raised to an inclination angle at a…

A: A particle of mass m rests on a plane. Now, the plane is raised to an inclination angle as shown in…

Q: Q2: 0 0 The Hamiltonian is represented by the matrix H = u 0 0 1 Where u is positive real number. 1…

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Q: dx dy Consider the Lagrangian L= a| +b dt dt +cxy, where a,b and c are constants. If P, and p, are…

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Q: Q2. For a simple pendulum of length t, the angle Obetween rest position and deflected position is…

A: We are given kinetic energy T and potential energy V of the system.

Q: 6. Consider a mass m which is constrained to move on the frictionless surface of a vertical cone…

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Q: ** Problem 3.23 Consider the following Hermitian matrix: 2 i 1 T = -i 2 i 1 -i 2 (a) Calculate…

A: This problem can be solved using the properties of eigenvalues & eigenvectors. det(T) = product…