Course guide of Quantum Physics (2671132)

Curso 2023/2024
Approval date: 23/06/2023

Grado (bachelor's degree)

Bachelor'S Degree in Physics




Fundamentos Cuánticos


Física Cuántica

Year of study



1 y 2

ECTS Credits


Course type

Compulsory course

Teaching staff


  • Marta Anguiano Millán. Grupo: A
  • Blanca Biel Ruiz. Grupo: B
  • María Cruz Bosca Díaz-Pintado. Grupo: B
  • Francisco Javier Gálvez Cifuentes. Grupo: A
  • María Rosario González Férez. Grupo: C
  • Daniel Rodríguez Rubiales. Grupo: C


  • Marta Anguiano Millán Grupo: 2
  • Blanca Biel Ruiz Grupo: 1
  • María Cruz Bosca Díaz-Pintado Grupo: 3
  • Pablo Canca López Grupos: 3 y 4
  • Francisco Javier Gálvez Cifuentes Grupos: 1 y 4
  • Juan Manuel García Garrido Grupos: 7 y 8
  • María Rosario González Férez Grupo: 1
  • María Elena López Melero Grupos: 5 y 7
  • Eugenio Megías Fernández Grupo: 2
  • Anderson Steven Peña Sabogal Grupo: 7
  • Daniel Puerta Megías Grupo: 6
  • Daniel Rodríguez Rubiales Grupo: 2

Timetable for tutorials

Marta Anguiano Millán

Ver email
  • Wednesday de 16:00 a 19:00 (Despacho)
  • Thursday de 16:00 a 19:00 (Despacho)

Blanca Biel Ruiz

Ver email
  • Tuesday
    • 11:00 a 13:00 (Despacho)
    • 15:00 a 17:00 (Despacho)
  • Thursday de 11:00 a 13:00 (Despacho)

María Cruz Bosca Díaz-Pintado

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  • First semester
    • Tuesday de 16:00 a 19:00 (Despacho)
    • Wednesday de 11:00 a 14:00 (Despacho)
  • Second semester
    • Tuesday de 11:00 a 14:00 (Despacho)
    • Wednesday de 11:00 a 14:00 (Despacho)

Francisco Javier Gálvez Cifuentes

Ver email
  • First semester
    • Monday de 11:00 a 13:00 (Despacho)
    • Wednesday
      • 10:00 a 12:00 (Despacho)
      • 17:00 a 19:00 (Despacho)
  • Second semester
    • Tuesday de 09:00 a 12:00 (Despacho)
    • Wednesday de 09:00 a 12:00 (Despacho)

María Rosario González Férez

Ver email
No hay tutorías asignadas para el curso académico.

Daniel Rodríguez Rubiales

Ver email
  • Monday de 11:00 a 13:00 (Despacho)
  • Tuesday de 16:00 a 18:00 (Despacho)
  • Wednesday de 17:00 a 19:00 (Despacho)

Pablo Canca López

Ver email
  • Tuesday de 09:00 a 12:00 (Despacho)
  • Wednesday de 15:00 a 18:00 (Despacho)

Juan Manuel García Garrido

Ver email
  • Monday de 11:00 a 13:00 (Despacho)
  • Tuesday de 11:00 a 13:00 (Despacho)
  • Wednesday de 16:00 a 18:00 (Despacho)

María Elena López Melero

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  • Tuesday de 18:00 a 20:00 (Despacho)
  • Wednesday de 18:00 a 20:00 (Despacho)
  • Thursday de 11:00 a 13:00 (Despacho)

Eugenio Megías Fernández

Ver email
  • First semester
    • Monday
      • 10:00 a 12:00 (Despacho)
      • 17:00 a 18:00 (Despacho)
    • Tuesday de 17:00 a 18:00 (Despacho)
    • Wednesday de 10:00 a 11:00 (Despacho)
    • Thursday de 10:00 a 11:00 (Despacho)
  • Second semester
    • Monday de 10:00 a 12:00 (Despacho)
    • Wednesday de 10:00 a 12:00 (Despacho)
    • Thursday de 10:00 a 12:00 (Despacho)

Anderson Steven Peña Sabogal

Ver email
  • Tuesday de 08:00 a 10:00 (Despacho)
  • Wednesday de 08:00 a 10:00 (Despacho)
  • Thursday de 08:00 a 10:00 (Despacho)

Daniel Puerta Megías

Ver email
  • Monday de 16:00 a 18:00 (Despacho)
  • Wednesday de 11:00 a 13:00 (Despacho)
  • Friday de 11:00 a 13:00 (Despacho)

Prerequisites of recommendations

It is recommended to have passed the following courses: Physics, Mathematical Methods, Linear Algebra and Geometry, Mathematics and Mechanics and Waves and desirable to have passed also the course Numerical Methods and Simulation.

Brief description of content (According to official validation report)

  • Origins of Quantum Physics. The wave function and the Copenhagen interpretation.
  • The Schrödinger equation and the time-independent Schrödinger equation.
  • One-dimensional problems.
  • Angular momentum. Three-dimensional problems with central potentials.
  • Approximate methods for stationary states.
  • Experimental techniques in Quantum Physics.

General and specific competences

General competences

  • CG01. Skills for analysis and synthesis
  • CG02. Organisational and planification skills
  • CG03. Oral and written communication
  • CG05. Skills for dealing with information
  • CG06. Problem solving skills
  • CG07. Team work
  • CG08. Critical thinking
  • CG09. Autonomous learning skills
  • CG13. Knowlegde of a foreign language

Specific competences

  • CE01. Knowing and understanding the phenomena of the most important physical theories
  • CE02. Estimating the order of magnitud in order to interpret various phenomena
  • CE04. Medir, interpretar y diseñar experiencias en el laboratorio o en el entorno
  • CE05. Modelling complex phenomena, translating a physical problem into mathematical language
  • CE07. Transmitting knowledge clearly, both in academic as in non-academic contexts
  • CE09. Applying mathematical knowlegde in the general context of Physics

Objectives (Expressed as expected learning outcomes)

The student will know and understand:

  • The quantum theoretical basis of modern physics.
  • The structure of quantum theory, its experimental support and its phenomenology.
  • The scales and orders of magnitude of physical phenomena.

The student will be able to:

  • Solve the given problems, applying the required mathematical and numerical methods.
  • Learn the basics of a physical process or phenomenon and establish a model to solve it, developing the pertinent approximations in order to reduce the original problem to a treatable level.
  • Initiate in new fields independently.
  • Acquire a knowledge of the discipline that allows them to model and understand the essential characteristics of the dynamics of microscopic systems.
  • Develop a critical thinking that allows them to build and test physical models, by incorporating new experimental data to the available models, verifying their validity and suggesting changes in order to improve the agreement between the models and the data.

Detailed syllabus



  1. Radiation and Matter: situation in Physics at the end of the 19th century. Black body radiation: classical theory and Planck's postulate.
  2. Particle nature of radiation: Photoelectric effect. Cathode rays. X-rays. Compton diffusion.
  3. Old atomic models: The Rutherford model. The Bohr model. The Franck-Hertz experiment. The Bohr-Sommerfeld model: quantization rules. The Zeeman effect.
  4. Wave nature of matter: matter waves: The de Broglie postulate. Experimental confirmation: The Davisson-Germer experiment.
  5. Wave-particle duality.


  1. The wave function, its equation and its probabilistic interpretation. Wave packets. Uncertainty Principle.
  2. The Schrödinger's equation and probability conservation. Position and momentum representation. Expected values. Ehrenfest's theorem.
  3. The eigenvalue equation of energy or time-independent Schrödinger equation. Quantization of energy. Time evolution of the states.


  1. Diffusion processes: Step potential. Potential barrier. Reflection and transmission coefficients. Tunnel effect.
  2. Bound states: Square well potentials. Harmonic oscillator.
  3. Potentials with deltas. Periodic potentials.


  1. Orbital angular momentum and spatial rotations.
  2. General theory of angular momentum. Matrix representation of angular momentum operators. Eigenvalues and eigenvectors. Spherical harmonics.
  3. The electron spin. The Stern-Gerlach experiment.
  4. Composition of angular momentum. Clebsch-Gordan coefficients. Total angular momentum.


  1. Separable variable potentials in Cartesian coordinates: free particle, three-dimensional square wells. The isotropic harmonic oscillator.
  2. Two-particle systems with central force. Coordinate separation. Radial equation and degeneracy. The free particle. Square wells. The isotropic harmonic oscillator.
  3. The hydrogen-like atom. Energy Spectrum. Spectroscopic notation. Spin-orbit interaction.
  4. Perturbation theory. Applications. Variational method. The Helium atom.


Exercise sessions:

  • Detailed resolution of a selection of problems associated with each of the topics.

Laboratory sessions:

Practice 0. Introduction to the Quantum Physics laboratory.

Practice 1. The charge-to-mass ratio of the electron.

Practice 2. The photoelectric effect.

Practice 3. Electron diffraction.

Practice 4. Atomic spectra.

Practice 5. The Franck-Hertz experiment.


Basic reading list


  • B.H. Bransden and C.J. Joachain, “Quantum Mechanics”; 2nd ed., Pearson; Dorchester, 2000.
  • C. Cohen-Tannoudji, B. Diu and F. Lalöe, “Quantum Mechanics”; 3 vols, Wiley-VCH, 2020.
  • A. Galindo y P. Pascual, “Mecánica Cuántica”; Eudema; Madrid, 1989 (advanced text book).
  • N. Zettili, "Quantum Mechanics: Concepts and Applications". 2º ed. Wiley 2009.
  • R. Eisberg y R. Resnick, “Física Cuántica”; Limusa, 1979.
  • L. D. Landau y E. M. Lifshitz, “Curso de Física Teórica. Vol. 3. Mecánica Cuántica (Teoría no-relativista)”; Reverté; Barcelona, 1978.
  • A. Messiah, “Mecánica Cuántica”; Tecnos; Madrid, 1973 (advanced text book).
  • P. Pereyra Padilla, “Fundamentos de Física Cuántica”; Reverté; 2011.
  • R. W. Robinett, “Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples”; 2nd ed., Oxford Univ. Press; 2006.
  • C. Sánchez del Río (coordinator), “Física Cuántica”; Eudema; Madrid, 1991.


  • A.Z. Capri, “Problems & Solutions in Nonrelativistic Quantum Mechanics”; World Scientific; 2002.
  • F. Constantinescu & E. Magyari, “Problems in Quantum Mechanics”; Pergamon Press; 1971.
  • A. Galindo y P. Pascual, “Problemas de Mecánica Cuántica”; Eudema; Madrid, 1989.
  • Y.K. Lim, “Problems and Solutions in Quantum Mechanics”; World Scientific.
  • Y. Peleg, R. Pnini and E. Zaarur, “Schaum´s Outline of Theory and Problems of Quantum Mechanics”; McGraw-Hill; 1998.

Complementary reading

  • D. Bohm, “Quantum Theory”; Dover; New York, 1989.
  • S. Brandt y H. D. Dahmen, H.D., “The picture book of quantum mechanics”; Wiley; 1985.
  • A.Z. Capri, “Nonrelativistic Quantum Mechanics”; 3º ed., World Scientific; 2002.
  • P. A. M. Dirac, “The Principles of Quantum Mechanics”; Oxford Univ. Press; Oxford, 1958.
  • R. Fernández Álvarez-Estrada y J. L Sánchez-Gómez, “100 problemas de Física Cuántica”; Alianza Editorial; Madrid, 1996.
  • R.P. Feynman, R.B. Leighton and M. Sands, “The Feynman Lectures on Physics. Vol. III. Mecánica Cuántica” (edic. bilingüe inglés-español); Fondo Educativo Interamericano; 1971.
  • S. Flügge, “Practical Quantum Mechanics”; 2nd ed., Springer; 1998.
  • S. Gasiorowicz, “Quantum Physics”; 3º ed., Wiley; 2003.
  • D.J. Griffiths, “Introduction to Quantum Mechanics”; 2nd ed., Pearson Prentice Hall; 2004.
  • C. S. Johnson y L. G. Pedersen, “Problems and solutions in Quantum Chemistry and Physics”; Dover; New York, 1986.
  • F. Mandl, “Quantum Mechanics”; Wiley; 2013.
  • J. Sánchez Guillén y M. A. Braun, “Física cuántica”; Alianza Univ.; 1993.
  • L. I. Schiff, “Quantum Mechanics”; 3º ed., McGraw; 1968.
  • G. L. Squires, “Problems in Quantum Mechanics with solutions”; Bangalore Univ. Press; 1997.
  • B. Thaller, “Visual Quantum Mechanics”; Springer; 2000
  • A. I. M. Rae, “Quantum Mechanics”; 5th. ed., Taylor & Francis; 2007.
  • Ta-You Wu, “Quantum Mechanics”; World Scientific; 1986.
  • F. J. Yndurain Muñoz, “Mecánica Cuántica”; 2º ed., Ariel; 2003.

Recommended links

Teaching methods

  • MD01. Theoretical classes

Assessment methods (Instruments, criteria and percentages)

Ordinary assessment session

  • The score of the exams corresponding to the contents of the first and second four-month periods will have a weight in the total grade of 50% and 40%, respectively. The remaining 10% of the total grade corresponds to the realization and evaluation of the laboratory practices.
  • At the end of the first four-month period there will be a partial exam corresponding to the contents of that period. Students who do not pass this exam (and those who want to improve their grade) will also have the option of taking it in the corresponding final ordinary exam.
  • The ordinary assessment session will consist of two exams: one for the evaluation of the each four-month period.
  • In order to pass the whole course, it is necessary to have a uniform and balanced knowledge of the whole subject. In particular, it will be required to perform and pass the laboratory practices. Additionally, a minimum of 4 out of 10 must be obtained in the evaluation of the contents of each of the four-month periods.

Extraordinary assessment session

  • The evaluation in the extraordinary assessment session will be carried out by means of three tests: one in which the contents of the first four-month period will be evaluated with a weight of 50% in the final grade, one devoted to evaluate the contents of the second four-month period, with a weight of 40%, and one to evaluate the laboratory practices, with a weight of 10%. However, those students who have passed the part of the exam associated with the laboratory practices will not have the obligation to repeat this part, maintaining in that case the grade previously obtained.

Single final assessment

  • The single final evaluation will be carried out by means of three tests: one in which the contents of the first four-month period will be evaluated with a weight of 50% in the final grade, one devoted to evaluate the contents of the second four-month period, with a weight of 40%, and the last one to evaluate the laboratory practices with a weight of 10%.