What are the expectation values of momentum (p) and p² of a particle in a 1-D box (infinitely hard walls) of dimension L?
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- A particle with mass m is in the state mx +iat 2h V (x, t) = Ae where A and a are positive real constants. Calculate the expectation value of (p).A neutron of mass m of energy E a,V(x) = Vo ) II. Estimate the kinetic energy of the neutron when they reach region III.10. A particle is represented (at time t = 0) by the wave function ¥(x,0) = {4(a² ¯ 0, JA(a²-x²), if- a ≤x≤+a otherwise (a) Determine the normalization constant A. (b) What is the expectation value of x (at time t = 0)? d (c) What is the expectation value of p (at time t = 0)? (Note that you cannot get it from p = m² .Why dt not?) (d) Find the expectation value of x². (e) Find the expectation value of p².
- Consider the wavefunction Y(x) = exp(-2a|x|). a) Normalize the above wavefunction. b) Sketch the probability density of the above wavefunction. c) What is the probability of finding the particle in the range 0 < x s 1/a ?Suppose a 1D quantum system is represented by the wavefunction in position space: (æ|2>(t)) = b(x, t) = Ae -3x+5it where it only exists () < x < ! Normalize the wavefunction, i.e., what is A?A particle is described by the wavefunction Ψ(t, x), and the momentum operator is denoted by pˆ. a) Write down an expression for the differential operator pˆ. b) Write down an expression for the expectation value of the momentum, ⟨p⟩. c) Write down an expression for the probability density, ρ. d) Write down an expression for the probability of finding the particle between x = a and x = b.