b): Consider two identical linear oscillators' having a spring constant k. The interaction potential is H = AxỊx2, where xi and x: are the coordinates of the oscillators. Obtain the energy eigen values.

Q: U(x) = U, e-x/a A particle of mass m moves in the one-dimensional potential x2 U(x) = U,

A:

Q: Let ƒ(x, y) = x² + 4y² and let C be the line segment from (0, 0) to (2, 2). You are going to compute…

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Q: 3. 2+i 2-i -31 A MATRIX GIVEN 15 1+し SHOW THAT THIS MATRIX IS HERMITIAN b) CALCULATE THE EIGENUALUES…

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Q: Find the expected ualue of the Harmonic oscillator function Un lx) =Nexp ( *z) Hn Lx)

A: it is required to find the expected value of the given harmonic oscillator function. Here the given…

Q: nic oscillator system. Hint:

A: Given: Hmn=12mx.2mn+12mω2x2mn

Q: Is the following total differential exact? df(g,h) = 7g(g^3+ h^2)jdg + 2h^4(3g^2 + 7h^2)jdh. Could…

A:

Q: Q5:1 A particle of mass m moves in a one dimensional potential U (x) where x a Sketch the…

A:

Q: Consider a particle of mass m moving in the following potential V(x)= vị for xv2. What is the grown…

A: The potential is specified as: Vx=v1 for x<0Vx=0 for 0≤x≤aVx=v2 for a<x≤aVx=∞ for x<2a…

Q: What is the energy of a particle restricted by an infinite square well and move along the interval 0…

A: In the infinite square well potential we have wavefunction and energy in the interval…

Q: Consider a particle of mass u, whose Hamiltonian is: p2 1 Ho = 27+R² Но (an isotropic…

A: Required to find the energy levels of the quantum system

Q: Example. Assuming that two similar partices, with coordinates n, and 2, have the combinal kineric…

A: The Hamiltonian for the given system is given as  H^=-h28π2m∂2∂x12+∂2∂x22The combined kinetic…

Q: 3. Find the differential cross-section for the scattering of particles by a central symmetry…

A: To find the differential scattering cross section of potential given above

Q: (4a³ 1/4 T xe-ax²/2, where a = μω ħ The harmonic oscillator eigenfunction ₁(x) = (a) Find (x²) for…

A: Harmonic oscillator eigenfunction Ψ1(x)=(4α3π)1/4 x e-αx2/2                α=μωħ

Q: A system with charge (number of electrons) is placed in an electric field with potential E (volts).…

A:

Q: For an object of mass m that moves in three dimensions and has potential of k (x² + y² +z² V(x,y,z)…

A: The object of mass m is moving in 3 dimensions and has potential V(x,y,z) = k2(x2+y2+z2).

Q: Sketch the phase portrait corresponding to the potential obtained in part (a).

A: Here, we plot the graph.

Q: energy levels En of the anharmonic oscillator in the first order in the pa- rameter 3 are given by:…

A: We can use the direct results here of expectation value of x4 in nth state.

Q: What does your result for the potential energy U(x=+L) become in the limit a→0?

A: We want to calculate lima→0qQ8πε0alnL+aL-a=qQ8πε0lima→0lnL+aL-aa

Q: Q2: A pendulum bob of mast m is suspended by a string of length / from a car of mass M which moves…

A: To determine: (a) The Lagrangian function  The mass of the pendulum is m, the length of the pendulum…

Q: A particle of mass 'm' is moving in a one-dimensional box defined by the potential V = 0,0<xsa and V…

A:

Q: Find the expressions for the car- tesian components and the angular momentum measure L = (Lx, Ly,…

A: Find the expressions for the cartesian components and the angular momentum measure L = (Lx, Ly, Lz)…

Q: PROBLEM 3. Using the variational method, calculate the ground s ergy Eo of a particle in the…

A: Given: The potential of the triangular well is as follows.   The trial function is Cxexp(-ax).…

Q: 10. P15.6) Show that the total energy eigenfunctions y210(r, 0,4) and y211(r, 0,0) are orthogonal.…

A: Using properties of the delta functions,

Q: 2) Consider a particle in a three-dimensional harmonic oscillator potential V (x, y, 2) = ;mw (x² +…

A: Let the given particle is the electron. Then the transition probability (W) be given as, Where, ω…

Q: Anisotropic Oscillator (Anisotropic Oscillator) is a kind Consider a rational two-dimensional…

A: Given,Considering two dimentional anistropic oscillator in x and y direction.For a two dimentional…

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: Find the energy eigen value of the particle

A:

Q: Show that the minimum energy of a simple harmonic oscillator is hω/2. What is the minimum energy in…

A: The mean value of x2av is the mean square devation ∆x2By substituting the mean square deviation…

Q: matrix element of p² be

A:

Q: Find the equilibrium positions of the following 1-dimensional potential energy function. Examine the…

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Q: Let's consider a harmonic oscillator. The total energy of this oscillator is given by E=(p²/2m)…

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Q: In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with particles or rigid…

A: ## The student has asked to answer 3.2 specifically!!

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: For a harmonic oscillator state |n⟩, determine  a. b. c. ΔxΔp

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Q: 7.11 (a) A crate slides partway up the ramp, stops, and slides back down. (b) Energy bar graphs for…

A: In the given example,  The problem based on the conservation of energy.

Q: Q1; Particle with mass m and energy E moving from left to right Give the eigen function which…

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Q: U = kgT²ðIn ZN %3!

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Q: the full-dimensional (3-D) control minimal realization.

A: Given that transfer function of linear lung mechanics model is, G(s)=ss3+3s2+2s

Q: Determine the polar equation for orbit r(0) of a particle in a potential energy field given by V(r)…

A: The Potential energy field is given by, here α and β are constants. V(r) = -αr+βr2 where α&gt;0 and…

Q: e normalization

A: