Show the matrix representation of the operators a. position (x) b. momentum (p) for the one-dimensional harmonic oscillator problem. (Hint: Connect with operators A and At)
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: Please solve part d,e,f A simple pendulum of mass m and length L is shown in the figure below. Take…
A: Given: A simple pendulum of mass m and length L. Potential energy at lowest point of…
Q: Show that for a particle in a box of length L and infinite potential outside the box, the function…
A:
Q: A system, initially in state li), is disturbed H' (t) = G sin wt with the time-independent G…
A: According to given data, system initially in |i> state experience disturbance H'=G sinωt The…
Q: All parts of this problem refer to the harmonic oscillator. A) Use the expressions for the operators…
A: Given data : Harmonic oscillator xˆ and pˆ are Hermitian operators To find : A) Use the…
Q: A system at initial time t= 0 with wave function p(x,0) = Ae¬alx| forces). propagates freely (no…
A: Given function, ψx,0=Ae-ax a. Normalization condition,…
Q: A good example of time evolution of an operator is the position in x in 1-dimension. This simplified…
A: The expectation value of x can be written as: where is the complex conjugate of .In classical…
Q: Which of a, b or c is most likely to be correct? J Hint: Romombor tho roguirod rtiog of rono
A: Wavefunctions Wavefunctions are mathematical functions that encode the properties of a particle. The…
Q: 1. Given that x(t) the coordinate operator for a free particle in one dimension. Evaluate [x(t),…
A:
Q: A particle of mass m moves in a potential of the form V(x)= 2 cx² cx4 where c is a constant.…
A:
Q: For the normalized wavefunction v(x)= V2 cos(2.xx ). find the expectation value of kinetic energy
A:
Q: POOL2_P.3) Show that the total energy eigenfunctions 100 (r) and 200 (r) are orthogonal.
A: We know that condition of orthogonal is <Ψ100lΨ200>=0 Hence using this condition we can solve…
Q: A simple pendulum of mass m and length L is shown in the figure below. Take the reference of…
A: Part (a) The given pendulum is constrained to move in the XY plane only. Hence z coordinate of the…
Q: 04 (12 Marks) (a) Given Y. P- ih, and H- (b) Let the wave function for the particle is p(z)-2 sin(…
A: [Y^, P^] = ih(cut) H^ = (p^2 ) / 2m
Q: Find the explicit matrix form for the three corresponding g*, Sz, 3x operators s=2 ?
A:
Q: Q4.1 Determine explicitly (i.e. give all the details of the derivation), the energy eigenvalues En…
A: Given, wavefunction ψ=2asinnπax
Q: You are given the transformation P = Bq² Q = ap q a. Find the partial derivatives of the old…
A:
Q: If the function is f(x)=cos x², find the result when we add the three operators to them. 1-position…
A:
Q: HO Eigenstate. Prove that the ground state wavefunction for the harmonic oscillator is an…
A: The square of the wave function is the chance of finding the oscillator at any given value of x. The…
Q: The Lagrangian for a one-dimensional harmonic oscillator is (a) kx 1 (b) mx2 (c) mx+ kx (d) mx + kx-
A: Here, we use the formula of Lagrangian to get the required.
Q: H.W. A one dimensional harmonic oscillator is described by the Hamiltonian Ĥ = ho â'௠+ -/-) as…
A:
Q: 1. Following is a 1D wavefunction that is associated with a particle moving between -o and +oo: (x)…
A: Let us find the given question demanding for, The normalizing constant A for the wave function,…
Q: Consider a particle in an infinite potential well. (+∞o x a a. Write down the form of the…
A:
Q: Problem B.3 Simple harmonic oscillator. We study the simple harmonic oscillator of an object of mass…
A: The detailed solution is following.
Q: a particle is confined to move on a circle's circumference (particle on a ring) such that its…
A:
Q: 1) Determine the lagrange polynomial of second degree that can be used to approximate F(1.5) based…
A: Given: The data is as follows: Introduction: Lagrange polynomial is a technique to determine a…
Q: 2. Show that the first two wavefunctions of the harmonic oscillator (McQuarrie Table 5.3, p. 170)…
A:
Q: Coupled Flarmonic Oscillators X2 : 0 ) Write down the 2nd law for each of the masses. Use…
A: We will only answer the first question since the exact question to be answered was not specified.…
Q: Question Four: For the simple pendulum Shown: If the string is an elastic one with elastic (force…
A:
Q: All problems from Goldstein. 1. Show that the function S=(q? + a*)cot(at) - maqa cse (st) is a…
A: The Hamiltonian-Jacobi equation be defined as, Hq,∂S∂q+∂S∂t=0
Q: a particle is confined to move on a circle's circumference (particle on a ring) such that its…
A:
Q: *Problem 4.34 (a) Apply S_ to |10) (Equation 4.177), and confirm that you get /2h|1–1). (b) Apply S+…
A: (a) As we know,S±=|s ms>=hs±mss±ms+1 |s ms±1>Here s=1 and ms=0,S-=|1 0>=h1-01-0+1 |1…
Q: A pendulum hangs from a fixed point, but the pendulum itself is a spring with a constant k and…
A: A pendulum which is a spring hangs from fixed point is as shown in the following figure. Since the…
Q: 7. Prove that a solution of the Neumann problem V²u = f in D u = g on B differs from another…
A:
Q: a particle is confined to move on a circle's circumference (particle on a ring) such that its…
A:
Q: Suppose a particle has zero potential energy for x < 0. a constant value V. for 0 ≤ x ≤ L. and…
A: The potential being described by the problem is known as a step potential
Q: A Hamiltonian is given in matrix form as ħ (wo W1 A₁ = 7/7 (@₂₁ 000) 2 a. What are the energy…
A:
Q: Wow  is a Hermitian operator. [p) is an eigenvector to Å with „cnvalue A . [ø) is also an…
A: (a) A^|ψ>=λψ (b) It is given that A is a Hermitian operator. A^+=A^ Evaluating :…
Q: For Problem 8.37, how do I find <1/r> within the integral? I think that the exponent function…
A: The radial wave function of 1s electron in hydrogen atom is.
Q: By employing the prescribed definitions of the raising and lowering operators pertaining to the…
A:
Q: Using what are canonical transformations ? generating function F=1m 009² cót @. Discuss the problem…
A:
Q: Prove that or Harmonic ascillator, the Hamiltonian Can be written as Ĥ = trow (ât.ât!)
A: The Hamiltonian operator when operated on a wavefunction, we get the energy for a state of the wave…
Q: 11. Evaluate (r), the expectation value of r for Y,s (assume that the operator f is defined as…
A: For hydrogen atom the ground state wavefunction is, ψ1s=e-ra0πa03/2 (1)where a0=0.0529nm…
Step by step
Solved in 2 steps with 2 images
