Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Homework 5 { PHYS 5450
Document related concepts
Quantum group wikipedia , lookup
Canonical quantization wikipedia , lookup
Coherent states wikipedia , lookup
Light-front quantization applications wikipedia , lookup
Double-slit experiment wikipedia , lookup
Casimir effect wikipedia , lookup
Atomic orbital wikipedia , lookup
Tight binding wikipedia , lookup
Feynman diagram wikipedia , lookup
Path integral formulation wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Quantum state wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Renormalization group wikipedia , lookup
Hydrogen atom wikipedia , lookup
Wave–particle duality wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Matter wave wikipedia , lookup
Wave function wikipedia , lookup
Particle in a box wikipedia , lookup
Probability amplitude wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Transcript
Homework 5 { PHYS 5450
[1] We consider the innite square
well of width a.
(a) Find the energies En and normalized wave functions n of the stationary states in terms of the quantum
number n
(b) Calculate the momentum representations n(p) of the stationary states. Manipulate your expression so
as to make it appear as a sum of two sinc functions: sinc(u) = sinu(u) .
(c) Make a graphical representation of the momentum probability densities for n = 1 and n = 2.
(d) Sketch the momentum probability densities for a large value of n.
(e) Using n(p) evaluate the expectation value of the momentum p
(f) Using n(p) write the expectation vale of p2 as an integral you will not attempt calculating.
(g) Using (x), calculate the expectation value of p2.
[2] Consider the wave
function j (t = 0) >= p12 [j1 > +j2 >].
(a) Write j (t) > using the Bohr frequency !21 = E2 h E1
(b) Calculate < x > (t). The calculation will be easier if consider x'=x-a/2 instead of x directly. Easier is
better.
(c) Calculate < H > and < H 2 > to estimate H the standard deviation of the energy. Then calculate
H 2!
