Problem #1 ---- -15pts- vvhat is the physical sense of the quantity Do in the expression...
What is the physical sense of the quantity po in the expression for the wave-function: *(x) = P(x) exp (1984) where the function (x) is real?
PRINT YOUR NAME (on every page) Midterm exam 32300 G-Introduction to Quantum Mechanics-Prof. Krusin Solve all 4 problems 15pts Problem #1 What is the physical sense of the quantity po in the expression for the wave-function: Cx) (x) exp ( ipox where the function (x) is real? 25ntc
Problem 2.6 Although the overall phase constant of the wave function is of no physical significance (it cancels out whenever you calculate a measurable quantity), the relative phase of the coefficients in Equation 2.17 does matter. For example, suppose we change the relative phase of ψι and in Problem 2.5: where ф įs some constant. Find ų,(x,t), Ux.t)12, and (x), and compare your results with what you got before. Study the special cases φ = π/2 and φ = π....
1. Starting with one of Newton's laws and your free body
diagram, derive an expression for the normal force exerted on the
block by floor.
- Assess you answer in the following way: If you
let \(\theta\) = 0, what does your
solution predict for the normal force? Does this make physical
sense?
2. Starting with one of Newton's laws and your free body
diagram, derive an expression for the coefficient of kinetic
friction \(\mu_{k}\) between the
block and the...
Problem Three (1) Write the expression that defines the expectation value of the operator <x> for any function Y. (II) Find the expectation value of <x> for the particle in a box defined by the wave function: Y=N(L x - X°) within limits ( < x < L. which you previously normalized in Problem Two on the previous page.
Problem 2 (15pts). Consider the following joint density function 0, else (a) Find the conditional density function of Y given X (b) Find E(Y|X). (c) Find Var(Y|x).
Problem 8 (30 pts). The ground state wave function for the hydrogen atom is: W... (7,0,) - (a, 15pts) Find (-2) for an electron in this state. Find <x> and <x>
Problem 8 (30 pts). The ground state wave function for the hydrogen atom is: W... (1,0,0) - (a, 15pts) Find (-) for an electron in this state. Find <x> and <p>
tthe-independent Help: The operator expression dimensions is given by H 2m r ar2 [2] A particle of mass m is in a three-dimensional, spherically symmetric harmonic oscillator potential given by V(r)2r2. The particle is in the I-0 state. Noting that all eigenfunetions must be finite everywhere, find the ground-state radial wave-function R() and the ground-state energy. You do not have to nor oscillator is g (x) = C x exp(-8x2), where C and B are constants) harmonic malize the solution....