Problem 04 A particle of mass m is in an infinite potential well of width a...

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Problem 04 A particle of mass m is in an infinite potential well of width a defined as V(x)= - {% -15*≤1 otherwise At time t = 0 the particle's wavefunction can is known to be (x,t= 0) = a(z) + 2(x) where (2) describes the ground state wavefunction and 2(2) describes the first excited state wavefunction. a) Calculate the expectation value of position at time t > 0 b) Prove that m(x) = (px) c) Compute the probability current inside the infinite potential well Note: A few integrals which you may find useful r sin² ([1/2]) dr=0 fa/2 Tin (-1/2]) sin (2π [-1/2])= 8a2 972 Problem 04 A particle of mass m is in an infinite potential well of width a defined as V(x)= - {% -15*≤1 otherwise At time t = 0 the particle's wavefunction can is known to be (x,t= 0) = a(z) + 2(x) where (2) describes the ground state wavefunction and 2(2) describes the first excited state wavefunction. a) Calculate the expectation value of position at time t > 0 b) Prove that m(x) = (px) c) Compute the probability current inside the infinite potential well Note: A few integrals which you may find useful r sin² ([1/2]) dr=0 fa/2 Tin (-1/2]) sin (2π [-1/2])= 8a2 972