Lecture 7 Notes
Particle nature of light was proposed by Einstein in 1905 to explain the photo-electric
effect. Photo-electric effect automatic door openers in grocery stores. Particles of light
are called light quanta or photons.
Energy of a Photon = h (
Lecture 4 Notes
Photons can be treated as packets of
light which behave as a particle.
To describe interactions of light with matter, one generally has to
appeal to the particle (quantum) description of light.
A single photon has an energy given by
E =
Lecture 3 Notes
Quantum theory is a theory needed to describe physics on a
microscopic scale, such as on the scale of atoms, molecules,
electrons, protons, etc.
Classical theories:
Newton Mechanical motion of objects (F = ma)
Maxwell Light treated as a wa
Physics 742 Graduate Quantum Mechanics 2
Final Exam, Spring 2010
Due Friday, May 7
You may use (1) class notes, (2) the text, (3) former homeworks and solutions (available
online), or (4) any math references, such as integral tables, Maple, etc, including
Physics 742 Graduate Quantum Mechanics 2
Solutions to Final Exam, Spring 2010
Due Friday, May 7
You may use (1) class notes, (2) the text, (3) former homeworks and solutions (available
online), or (4) any math references, such as integral tables, Maple, e
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 6
1. [10] For the finite square well in section C, we showed that (6.24) is satisfied for
the even wave functions. Repeat this derivation for the odd wave functions; i.e.,
derive (6.25).
We kno
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 5
1. [15] The Lennard-Jones 6-12 potential is commonly used as a model to describe
the potential of an atom in the neighborhood of another atom. Classically, the
12
6
energy is given by E 1 mx
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 3
1. [10] Prove Schwartzs inequality, , , , , . You may prove it
however you want; however, here is one way to prove it. Expand out the inner
product of a b with itself, which must be positive,
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 2
1. [10] A free particle of mass m in one dimension takes the form at t = 0
x, t 0 x A exp iKx 1 Ax 2
2
1/ 4
Note that this is identical with chapter 1 problem 4. Find the wave at all
subseq
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 1
1. [10] A particle of mass m lies in one-dimension in a potential of the form V(x) =
Fx, where F is constant. The wave function at time t is given by
x, t N t exp 1 A t x 2 B t x
2
where N,