Homework set-1 and study help

1.&n= bsp; (a) Calculate the energy of photons, electrons, neutrons, in electron volts, wh= en their de Broglie wavelength is 1⁰A. Such a wavelength is useful for pr= obing the structure at the atomic scale.

You can simplify the calculation if you use the resource from the link in the n= ext problem.

(b) The diffract= ion of C_60,the fullerine,= or buckeyball, has been observed in experiments. = Read the original paper in Nature, 401, 680 (1999), ( Article ). Summarize the paper using less than 300 words.

2.&n= bsp; When dealing with electrons, one often uses = the atomic units to describe physical quantities. In atomic units, you set m=3D= e=3D= =3D1. Common physical quantities like length, time, energy etc are then expressed in a= tomic units as well. Here is a good link that you may want to save

h= ttp://www.phys.ksu.edu/personal/cdlin/mainpage/atomic-units.mht

Use the link above, do the following calculations. Express the quantitites in atomic units.

Find the numbers from books or web resources.

(a)&= nbsp; The energy separation between the 1s and 2p levels of atomic hydrogen.

(b)&= nbsp; The fine structure separation of the 2p_1/2 and 2p_3/2 level= s of atomic hydrogen.

(c)&= nbsp; The separation between 2s_1/2 and = 2p_1/2levels in atomic hydrogen. (This is called Lamb shift.)

You can fi= nd accurate data for H from http://physics.= nist.gov/PhysRefData/HDEL/data.html

3.&n= bsp; Describe in words the Hilbert space and its dimension, the basis state vectors, and some examples of operators and what= can be measured, for the following systems.

(a) An electron with spin 1/= 2 in a magnetic field.

(b) A particle of mass m is confined to an infinite square well potential.

(d) Two noninteracting particles of ma= ss m₁ and m₂ confined in an infinite square well potential.=

Review and = Preview –

Review part=

1.&n= bsp; Quick review of Planck distribution law or black-body radiation

See&= nbsp; htt= p://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

http://hyperp= hysics.phy-astr.gsu.edu/hbase/mod6.html

&nbs= p; 3D"http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod/planckrf.gif"

&nbs= p; 3D"http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod/planckrw.gif"

Exercise: use the graph here http://en.wik= ipedia.org/wiki/File:Firas_spectrum.jpg. It shows the cosmic microwave background spectrum measured from COBE. Calculate the average isotr= opic temperature of the universe based on the above graph. (The anisotropy is in= the order of 10^-4 to 1= 0^-5 from modern meaurements).

1.&n= bsp; Quick review of Compton scattering

See http://hyperphysics.phy-astr.gsu.edu/= Hbase/quantum/compdat.html#c1

The resulting formula

= &nb= sp; 3D"http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/imgqua/compeq8.gi=

The derivation is straightforward, bu= t a quick review is good for you.

see = http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/compeq.html#c1

Exercise: What is the Compton wavelength? In Angstroms.

Question: In what spectral region (microwave up to gamma-ray) should you worry about Compton scattering?

Here is a graph of the spectral range=

htt= p://en.wikipedia.org/wiki/File:Electromagnetic-Spectrum.png

While we are on this topic, you may w= ant to take a look at the transmittance or opacity of our atmosphere from this graph

http://en.wikipedia.org/wiki/File:Atmospheric_elec= tromagnetic_transmittance_or_opacity.jpg

2.&n= bsp; Double slit interference experiment with single electrons

A sketch of this experiment is descri= bed here http= ://www.hitachi.com/rd/research/em/doubleslit.html

A video clip of the electron “buildup” can be seen by clicking the link right below the figu= re there. The original paper is published in Tonomura et al, Am. J. Physics 57, 117-120 (1989).

Double-slit electron diffraction was = ranked as the most beautiful physics experiment by physicists. Here is the top 10 list:

See&= nbsp; = http://physics-animations.com/Physics/English/top10.htm

First evidence of electrons as waves = was carried out in the

Davisson-Germer experiment, see

ht= tp://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/davger2.html

Review what is the Bragg’s diffraction law

Here= h= ttp://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/bragg.html#c1

Preview:

In quantum mechanics, we fir= st have to deal with Hilbert space. Hilbert space is generalized from the linear vector space.

Quick review of the properties of a Vector Space

See       http://en.wikipedia.org/= wiki/Vector_space

In particular, the definition; axiom of additions; bas= es; dimension; matrices; eigenval= ues and eigenvectors; norm; inner product (scalar product)

        =          Later: direct product and direct sum

Qucik preview of polarization of light

See = http://en.wikipedia.org/wiki/Photon_polarization=

And look at : Jones v= ector; linear polarization; circular polarization;

         Energy, momentum and angular momentum of photons