Prove that the momentum operator of a free body is conserved or constant
Q: A massless spring of unextended length b and spring constant k connects two particles of masses mị…
A: Given that m1 and m2 are masses and k is the spring constant. l is the extended lenght. To explain…
Q: Prove that the kinetic energy operator is Hermetic
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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: (b) An clastic string AB of natural length 2 m has the end A fixed. A load of mass 4kg is attached…
A: →Let AB be the string of length 2 m with mass 4 kg attached at B which is rotating at a speed…
Q: we have Â* = -AÂ. A
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Q: Consider two vector fields X and Y and an arbitrary smooth scalar function f(x). The Lie derivative…
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Q: show hamiltonian operator for the plane waves (exponential, imaginary) Prove that this operator does…
A: The questions are: a) show Hamiltonian operator for the plane waves (exponential, imaginary). b)…
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: 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 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: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…
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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: Find the following commutators by applying the operators to an arbitrary function f(x) [e, x+d²/dx²]…
A: Given Data:The first commutator is [ex,x+d2dx2]And the second commutator is [x3−ddx,x+d2dx2]The…
Q: Consider a spin-1 particle with Hamiltonian Ĥ = AS² + B(Ŝ² − S²). Assume B < A, treat the second…
A: The unperturbed Hamiltonian for a spin-1 particle is: H_0 = AS_Z^2 where S_Z is the z-component of…
Q: Consider the Hermitian operator  that has the property Â4 = 1. What are the eigenvalues of the…
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Q: Consider the following Hamiltonian with constant m, n, and k, suppose that at t = 0 the system is at…
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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: The Hamiltonian of a certain system is given by 1 0 0 H = hw|0 0 0 Lo 0 1 Two other observables A…
A: Given: The Hamiltonian of the system is
Q: (d) What is AE for this system? (e) Let At denote the time it takes for the system to evolve from…
A: The Hamiltonian of the system is H = ℏω |1><1| Where ω = Constant frequency
Q: For an operator to represent a physically observable property, it must be Hermitian, but need not be…
A: Given that- For an operator to represent a physically observable property,it must be hermitian,But…
Q: 2.32 Consider a harmonic oscillator of mass m undergoing harmonic motion in two dimensions x and y.…
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Q: Prove that the vector field F(x,y,z) = (x^2 + yz)i − 2y(x + z)j + (xy + z^2)k is incompressible, and…
A: We have been given a vector field and we need to show that its incompressible and also need to find…
Q: Prove that the momentum operator of a free particle is a constant
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Q: Consider the time-independent two-dimensional velocity field u(x, t) = (−y, x, 0)in Cartesian…
A: Consider the time-independent two-dimensional velocity field u(x, t) = (−y, x, 0)in Cartesian…
Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…
A: The Hamiltonian is just the total energy of the system. That means it is the sum of Kinetic energy…
Q: What is a cyclic coordinate? Using the lagrange's equation of motion for a conservative system,…
A: A coordinate that does not explicitly appear in the lagrangian is referred to as cyclic coordinate.…
Q: A particle of mass m moves in the one-dimensional potential x2 U(x) = U, 7 Sketch U(x). Identify the…
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Q: Consider the uniform motion of a free particle of mass m. The Hamiltonian is a constant of the…
A: Given: The quantity is given as F(x, p, t) = x − pt/m
Q: Show that the eigen functions of the Hamiltonian operator are orthogonal and its eigen values are…
A: Hermitian Operators:An operator is said to be Hermitian if it satisfies: A†=ASuppose |am> be the…
Q: A particle of mass m oscillates in a vertical plane suspended by a massless string that goes through…
A: Let the angle between the string and the vertical be θ. The Lagrangian for the system is given by:…
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 operator  such that for function f(x) we have: Äf(x)= f(x+a)+ f(x-a). The domain for…
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Q: The Hamiltonian of a three-level system is represented by the matrix 22 Vo 2V + 1 22 H = 3V where Vo…
A: Hey dear this is related to perturbation theory have a look at solution
Q: Problem 9. For a system described by the Hamiltonian H = p²/2m + V(x), obtain an expression for d (p…
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Q: all and the floor are friction-less, the ladder will slide down the wall and along the floor until…
A: A ladder of length L and mass M is leaning against a wall. Assuming the wall and the floor are…
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: If we have two operators A and B possess the same common Eigen function, then prove that the two…
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Q: With the help of the commutation relation and the momentum operator [ x , P ] = i , if the function…
A: The commutator relation is given as : x,p=ih This gives p,x=-ih The momentum operator is defined as…
Q: Let there be two operators, Â = and V²(x, y, z) = + + ₂. Which of the following functions are…
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Q: A particle of mass m is forced to move on the inner surface of a smooth cone with side-peak angle α.…
A: The generalised co-ordinates are r and θ At any instance the position of the particle is given by :…
Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…
A: The value of ∆D is calculated as ∆D=D^2-D^2 Where D^2 is the expectation value of the D^2 operator.…
Q: Prove that the momentum operator is interchangeable with the total energy operator.
A: We know that moment operator and total energy operator is interchangeable. We can prove it as…
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