Luis Sánchez, currently an undergraduate physics student at Universidad de Guadalajara. My current research is in the area of interstellar molecular clouds (where star formation takes place) under the direction of Susana Lizano (at CRyA), we have preliminary results of the analytic expression that governs the photon flux in ionized regions with density gradients.
You can follow my adventures here.
Luis, receive this little award for your efforts to take afar the name of the U de G abroad:
Quantum mechanics 101
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Our local effort for a quantum mechanics course, mostly based on the books by Shankar, David Griffiths and Luis de la Peña.
This a list of topics we have covered this far:
Feb 22 (Griffiths, Ch. 1)
- Schrödinger equation
- Probabilistic interpretation of the wave function (Born probability)
- Position operator
- Momentum operator
Problem set: OCW 5
Feb 26 (De la Peña, Ch. 3)
Problem set: Gasiorowicz: 3.8, 3.9, 3.10, 3.12, 3.15
March 1 (Shankar A.2, de la Peña Ch. 4, Griffiths 2.4):
- The gaussian integral
- The free particle
- Fourier's technology (Fourier transform)
Problem Set: [freepart.pdf]
March 5 (De la Peña 4.2, Park 2.5)
- Born normalization
- The momentum operator revisited
- Problem solving session
Problem Set: [repmomental.pdf]
March 12 (Shankar 5.4)
- Bound states
- Scattering states
- Potential step
- Scattering states of the finite potential well
Problem Set: [wells.pdf]
March 15 (Griffiths 2.5, De la Peña 4.3, 4.4)
- Dirac's delta
- Delta function potential and barrier
- Dirac's normalization of the free particle
- Propagator of the free particle
Problem Set: [delta.pdf]
Because this lecture was particulary abstract I am posting here the lecture notes: [1],[2],[3]. You can also read about the free particle propagator in pag. 68 of Baym.
March 22 (Griffiths 2.3, De la Peña 11.2)
- Frobenius method
- Quantum harmonic oscillator: "brute force method".
As promised, here is the Mathematica notebook so you can now "wag the dog" yourself: [wagthedog.nb]
March 26 (Griffiths 2.3, de la Peña 11.4)
- Ladder operators
- Heisenberg picture of the harmonic oscillator
- Coherent states (if time permits)
Problem Set: [ho.pdf]
Now on: Formalism of quantum mechanics, you will need a working knowledge of linear algebra so read (Shankar Ch 1 or Griffiths 3.1 and 3.2).
April 16 (Griffiths 3.1, A.1, A.2, Shankar: 1.1, 1.2, 1.3)
- Vector spaces of finite dimension.
- Hilbert space
Problem Set: [LA.pdf]
April 19 (Sakurai 1.2, Griffiths 3.2, 3.6)
Problem Set: [dirac.pdf]
April 23 (de la Peña 9.1, 9.2)
- Pictures of a quantum system (Heisenberg picture, Schrodinger picture)
April 27 (Griffiths 3.2, 3.3)
- Determinate states
- Eigenfunctions of hermitian operators.
- Generalized uncertainty principle
Problem Set: [dyn.pdf]
May 7 (Shankar Ch 8, Park 6.1)
- Path integral formulation of quantum mechanics.
- Degeneracy in bidimensional systems.
Problem Set: [degeneracy.pdf]
May 10
- Symmetric states and Antisymetric states
- Gauge Transformations
Lecture notes [potentials.pdf]
May 21
- Angular momentum
- Conmutation relations of angular momentum
- Ladder operators for angular momentum
May 25
- Eigenvalues of angular momentum
- Eigenfuctions of angular momentum (Spherical harmonics)
Problem Set: [angmom.pdf]
May 28
New seminar: Principles of electrodynamics
editI am planing to launch a seminar on electrodynamics that follows the superb text by the same name by Melvin Schwartz. Some other good books are the ones by Wagness or Lorrain, Corson. Of course we will work a bit on Jackson and Greiner.
If you want to attend leave a message. I am particulary interested in volunteer lecturers.
Expected level: Vector calculus and second rank tensors. The first chapter of Schwarz should be enough, no previous knowledge of PDE's is expected. A little exposure on special functions, particulary Legendre functions and Spherical harmonics. Relativistic kinematics will be used in the middle part of the seminar.
Overall organization
- Electrostatics (this should be a rather fast review)
- Special techniques (Separation of variables, method of images and multipolar expansion)
- Relativistic kinematics (again, just a fast review)
- The "miracle" of magnetism
- Maxwell equations
- Magnetostatics
- Electrodynamics I (Faraday's Law, Displacement Currents, Boundary Conditions)
- Electromagnetic waves
- Electrodynamics II (Gauge transformations, Retarded Potentials, more on relativistic EM)
- An additional topic if time allows (maybe radiation, EM waves on matter or variational formulation of electrodynamics)
Curso de astronomía general
editVeremos 2 temas: mecánica celeste y un poco de óptica. La bibliografía recomendada es
- Fundamental Astronomy por H. Karttunen, P. Kröger, H. Oja, and M., Poutanen.
- An Introduction to Modern Astrophysics (2nd Edition) por Bradley W. Carroll and Dale A. Ostlie.
- Physical Universe: An Introduction to Astronomy (Series of Books in Astronomy) por Frank H. Shu.
Todo lo necesario en mecánica y matemáticas para el material del curso se puede consultar en
- Mathematical Methods in the Physical Sciences por Mary L. Boas.
- Kittel, Charles et al., "MECANICA", Berkeley Physics Course - Volumen 1, ed. Reverte
- Classical Dynamics of Particles and Systems por Stephen T. Thornton and Jerry B. Marion.
En concreto lo que necesitas saber es: momento angular, fuerzas centrales, formulación lagrangiana de la mecánica y el vector de Runge-Lenz, las matemáticas necesarias son más bien elementales, cálculo vectorial, integrales elípticas (eso lo veremos rápido en clase) y funciones de Bessel.
Algunos temas que se vieron muy ligeramente y clase e indudablemente ocuparán son:
- Propiedades de una elipse.
- Momento de inercia.
En resumen:
- Recordamos el movimiento circular uniforme, vimos que solo existe una fuerza en tal movimiento y apunta hacia el centro. Toda fuerza a distancia es central (por la tercera ley de Newton).
- Simplificamos el problema de los 2 cuerpos mostrando que de las 12 variables de entrada, solo 2 no se obtienen de una ley de conservación. Moviendonos al marco del CdM solo ocupamos 6 entradas, (despues veremos que 5 son invariantes).
- Obtuvimos las ecuaciones de movimiento, momento angular y energía.
- Demostramos las 3 leyes de Keppler. Para resolver la geometría de la órbita hay 3 métodos diferentes (al menos que yo conozca): Resolver la ec de movimiento (esto se hace en Kartunnen, lo tienen como copias), Acoplar las ecuaciones de conservación de momento angular y energía y resolver la ecuación resultante (esto se hizo en clase), usar el vector de Runge-Lenz (lo veremos en una clase pronto).
- Mostramos como calcular y para una órbita cerrada, vimos que las órbitas círculares tienden a maximizar tanto la energía como el momento angular, es por esto (las configuraciones que ocurren en la naturaleza tienden a minimizar la energía) que pese a ser las más simples, las órbitas circulares no son comunes.
