by using the annihilation operator prove that the wave function of ground state for harmonic oscillator is : -mw Yo = Ae 2h x²

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Q: A quantum mechanics problem Schrödinger's equation in the absence of a potential is h² 2m -V²=E, (1)…

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Q: Find the expectation value of the momentum for the particle in the state, W(x, ) = Ae'lx- wt)

A: Given that  ψx,t=Aeikx-ωtψ*x,t=A-ikx-wt ∫ψ*ψ dx =∫Ae-ikx-wtAeikx-ωtdx A2∫dx =1 p=∫-∞∞ ψ*x,t h2πid…

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Q: What is the first excited state energy for a square well potential (with V = -10 hartrees and a…

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Q: els wave function,

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Q: (WF-2) The wave function for a proton moving in 1D is given by: y(x) = Csin(x) for 0 ≤ x ≤ñ and zero…

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Q: (a) For the 1s wavefunction, calculate the probability for the electron to be found within the…

A: (a) 1s wave function is given as,ψ100(r)=1πa03e-r/a0Probablity of finding electron within the…

Q: The energy eigenvalues of a particle in a 3-D box of dimensions (a, b, c) is given by ny E(nx, ny,…

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Q: Starting with the time-independent Schrodinger equation, show that  = 2m.

A: The  time-independent Schrodinger equation is given by: Hψx=EψxH=p22m+u(x)

Q: a) Write down the one-dimensional time-dependent Schro ̈dinger equation for a particle of mass m…

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A: The objective of the question is to find the time Tπ, which is the time it takes for a spin-1/2…

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Q: An electron is trapped in a one-dimensional region of width 0.062 nm. Find the three smallest…

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Q: An electron is trapped in a one-dimensional region of width 0,05 nm. Find the three smallest…

A: Energy for a particle confined in a one dimensional well is- En=n2π2ℏ22mL2    =n2E0where…

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Q: = Consider a particle with mass m in an infinite square well of width L = 1, with energy E (a) What…

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