Find the energy eigen value of the particle

Q: A proton is contained in an infinite one-dimensional box with a minimum kinetic energy of 7.9 MeV.…

A: Solution:-Given thatminimum kinetic energy (KEmin)=7.9 MeV

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…

Q: Show that ugr correctly represents the velocity of the particle both relativistically and…

A: For non-relativistic case: ugr=dEdp=ddpp22m                    ∵E=p22m=2p2m=pmugr=v Therefore, in…

Q: For a 1D single particle, classical mechanics requires 2 values at time t to fully represent the…

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Q: The range, R, is defined as the horizontal distance a projectile travels when it returns to its…

A: Given data: Range of projectile motion  R =v022×sin2θ Required:  Value of θ when range is maximum

Q: Write down an expression for the probability density ρ(t, x) of a particle described by the…

A: It was said that a wave is associated with every matter. But wave needed to have something of…

Q: Show that exp(i*m*phi) is an eigenfunction of L(hat)z and find the corresponding eigenvalue

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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: eigen values.

A: I can guide you on how to approach solving the Schrödinger equation for the potential V(x) = |x|…

Q: (a) Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a…

A: a) The required uncertainty in energy is,

Q: Show that if (x) and (x) are solutions of the time independent Schrödinger equation, Y(x,t) =…

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Q: A particle has a lifetime of 1 × 10–23s. Calculate the typical uncertainty in the measurement of its…

A: Lifetime of the particle is t = 10-23 s

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…

Q: Suppose a particle has a wavefunction (x) = Ae² ekr (a) Find A so that this wavefunction is…

A: Normalized wave function: A wave function which satisfies the following conditions,…

Q: View the particle system in a one-dimensional box in the range - ≤ x ≤ of m-mass and q- charged…

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Q: in quantum mechanics ; calculate the eigenvalue of these operators L2 , Lz when l equal to 6 ?

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Q: Q3. Gerry & Knight Ch.2 2.3 Use The Baker-Hausdorf formula to show that the time dependence of the…

A: Solution: Q5. The position expectation of the wavefunction is calculated as: x=x<ψ01ψ01>…

Q: Show the relation LxL = iħL for the quantum mechanical angular momentum operator L

A: An operator in quantum mechanics is different from linear operators as here a function is applied on…