8. Find u an exponential solution for the Schrodinger equation iu,(t, x) + Au(t, x)=0, xERN, t≥ 0. Does u present dissipation or scattering?

Q: 1. A particle of m moves in the attractive central potential: V(r) = ax6, where a is a constant and…

A: Ans 1:  (a) A=(π2b​)1/4. (b) E(b)=2mbℏ2​+64b315α​. (c) bmin​=(32ℏ245αm​)1/4. (d)…

Q: An electron is the Spin State. X - B() י ו - 2i) %3D 3+i a. ind the Normalization constant B and the…

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Q: 32. Check the normalization of ψ0 and ψ1 for the harmonic oscillator and prove they are orthogonal.…

A: To find the normalization constant C0 and C1 and check the orthogonality of the two wavefuction

Q: A particle of mass m, which moves freely inside an infinite potential well of length a, is initially…

A: Given: ψ(x,0)=35asin3πxa+15a sin5πxa For the wavefunction at a later time t we have;…

Q: 3a.3. Consider a longitudinal wave us propagating in a linear monoatomic chain of mass M and with…

A:

Q: > show that the time independ ent schrodinger equation for a partide teapped in a 30 harmonic well…

A: Solution attached in the photo

Q: 2. Find the best bound on Es for the one-dimensional harmonic oscillator using the trial wave…

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Q: Which is the Schrodinger equation for a 1D harmonic oscillator:

A: The harmonic oscillator Hamiltonian is given by, H=p22m+12kx2 Here, m is the mass, k is the force…

Q: Show that the hydrogen wave functionsφ 200 and φ21-1 are normalized. If the integrals required are…

A: Given:-              ψ200= R20 Y002-ra0e-τ2a02a03212π      = 12π2a0322-ra0e-τ2a0 If ψ200 is…

Q: -h? d? 3. Find average value of kinetic energy, for ground state of the harmonic 2µ dx? ocillator.…

A: We have to use some basic formula here

Q: 1. A particle of m moves in the attractive central potential: V(r) = ax6, where a is a constant and…

A: The objective of the question is to compute the normalization constant A, calculate the ground state…