Show that the momentum operator in the position representation is given in the form: er d p=-ih-+ f(x) dx Where f(x) is a real function which does not affect the value of the commutator
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: 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: Consider the following unattached spring system. m₁ = 1, C₁ = 14, m₂ = 7 Write the stiffness matrix…
A: “As per the policy we are allowed to answer only 3 subparts at a time, I am providing the same.…
Q: we have Â* = -AÂ. A
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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: 2 ô Consider operator Ô 1 and function R(r)= e br. What must be the r ôr value of constant b for…
A: The operator is given as, O^=-∂2∂r2+2r∂∂r-1r The function is given as, R(r)=e-br Applying the…
Q: Show that for a particle in a box of length L and infinite potential outside the box, the function…
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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 hermitian operator H that has the property that H¹ = 1 What are the eigenvalues of the…
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Q: () = 1- (器)
A: we can explore the properties of Hermitian operator to prove the following statements. Let the…
Q: Straight Wire Segment A straight wire segment of length I makes an angle of 23 degrees with respect…
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Q: Consider the Hermitian operator  that has the property Â4 = 1. What are the eigenvalues of the…
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Q: Evaluate the commutator [*, Î], where is the operator for position and I is the operator for kinetic…
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Q: Consider the Hamiltonian Ĥ = ¸+ Ĥ' where E 0 0 Ĥ₁ 0 E 0 and Ĥ' is the time independent perturbation…
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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: 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: (a) Show that for a Hermitian bounded linear operator H: H → H, all of its eigen- values are real…
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Q: Consider if [Lx, A] = 0 and [Ly, A] = 0 where A is an operator and Lx and Ly are components of…
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Q: show that linear and position operators do not commute yes, linear
A: The question is not written clearly Some of the linear operator commutes with position operator But…
Q: commutator
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Q: H.W. A one dimensional harmonic oscillator is described by the Hamiltonian Ĥ = ho â'௠+ -/-) as…
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Q: Show that if  is a Hermitian operator in a function space, then so is the operator Ân, where n is…
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Q: Show that a covariant definition of the energy (valid in any reference frame) is E = -P#Uµ. (This…
A: Uμ = Four velocity = dxμdτ a contra varient tensor of rank 1 and we know , dτ = dtγ Now Uμ…
Q: Show that projection operators are idempotent: P2 = P. Determine the eigenvalues of P, and…
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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: 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: For a particle confined on a ring (with periodic boundaries) the appropriate wavefunction and…
A: Given: Hamiltonian operator = H^ = -ℏ22Id2dϕ2ψml(ϕ) = eimlϕ2π1/2
Q: What is the value of the commutator [Sy , ž]? Here Jy is the y-component of the angular momentum…
A: using different properties of commutator we can solve the question
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: (d) Consider the arbitrary ket |u)=i-1 uli), where i) is an orthonormal basis. i. Show that u =…
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Q: Prove that the eigen value of hermitian operator are real.
A: Let λ be an eigen value of hermitian operator in the state described by normalized wave function ψ.…
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: In a three-dimensional vector space consider an operator M in 2 0 ivz orthonormal basis {|1), |2),…
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Q: Show explicitly how to construct the L^3 operator. Then determine if the spherical harmonics (Yl,m)…
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Q: 2. Prove the followings: (Note: A = A,e, & e,)
A: ∇=∇kl ek⊗elA=Aij ei⊗ej Here we have to do tensor contraction of indices. Indices j & l can be…
Q: Prove that the kinetic energy operator is Hermitian
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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: Let Y alm Y = denote the eigenfunctions of a Hamiltonian for a spherically symmetric potential V(r).…
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