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Statistical Mechanics and Foundations of Quantum Mechanics (2025/2026: Semester 2 – Spring)
Cursusdoel
After completing this course students are able to:
- apply the laws of thermodynamics to simple processes and systems;
- describe how the fundamental relations of thermodynamics are derived from the principles of statistical mechanics;
- explain the fundamental probabilistic definition of entropy and its relation to irreversibility and the second law of thermodynamics;
- relate the concepts of energy, work, heat, entropy, enthalpy, free energy to each other, and understand the role played by intensive thermodynamic parameter such as temperature, pressure and chemical potentials in the study of systems in thermodynamic equilibrium;
- distinguish the different types of thermodynamic ensembles, calculate their partition functions in simple model systems, and derive thermodynamic relations;
- demonstrate the equivalence of the different types of thermodynamic ensembles;
- discuss the postulates of quantum mechanics and explain why quantum mechanics provides a more fundamental formulation of statistical mechanics;
- apply the operator formulation of quantum mechanics and use the Dirac notation to the study of simple systems;
- solve the one-dimensional quantum harmonic oscillator and describe the role of creation and annihilation operators.
| Description of assignment | Assesses course aims |
| Mid-term exam Assignments Final exam |
1, 2, 3, 4, all course aims 4, 5, 6, 7, 8, 9 |
Vakinhoudelijk
In this course you learn how to formulate the statistical description of a gas in thermodynamic equilibrium as a system of many weakly interacting particles. From this formalism, when applied to simple systems, you derive some well-known empirical thermodynamic laws relating quantities such as temperature and pressure, known as equation of states and Maxwell relations. You will be introduced to the concept of entropy and its relation to the famous second principle of thermodynamics. Entropy is discussed from its original introduction in the study of the Carnot cycle to its probabilistic definition introduced half a century later by Boltzmann.
In the last third of this course you are introduced to quantum mechanics starting from its postulates and shown how to arrive at the well known Heisenberg uncertainty relations. This approach is used to study simple systems. We also discuss why the quantum mechanical description of the physical world provides a more well defined way of applying the formalism of statistical mechanics to nature.
In the last third of this course you are introduced to quantum mechanics starting from its postulates and shown how to arrive at the well known Heisenberg uncertainty relations. This approach is used to study simple systems. We also discuss why the quantum mechanical description of the physical world provides a more well defined way of applying the formalism of statistical mechanics to nature.
Format
The course consists of four weekly contact hours, over 15 weeks. About 3/4 of this time consists of interactive lectures and the remaining of problem solving sessions..
The course consists of four weekly contact hours, over 15 weeks. About 3/4 of this time consists of interactive lectures and the remaining of problem solving sessions..
Werkvormen
UCU SCI 2 course
Toetsing
Spin part essay
Verplicht | Weging 10% | ECTS 0,75
Statistical mechanics assignments
Verplicht | Weging 25% | ECTS 1,88
*midterm FEEDBACK*
Niet verplicht
Spin part assignment
Verplicht | Weging 25% | ECTS 1,88
Statistical mechanics exam
Verplicht | Weging 40% | ECTS 3
Ingangseisen en voorkennis
Ingangseisen
Er moet voldaan zijn aan de cursus:
En er moet voldaan zijn aan minimaal één van de cursussen:
- [UCSCIPHY13] Introduction to Wave Phenomena in Nature
- [UCSCIPHY14] Introduction to Wave Phenomena in Nature - enhanced
Voorkennis
[UCSCIMAT11] Calculus and Linear Algebra is recommended
Voertalen
- Engels
Competenties
-
Interdisciplinariteit
Cursusmomenten
Gerelateerde studies
Tentamens
Er is geen tentamenrooster beschikbaar voor deze cursus
Verplicht materiaal
-
BOEKConcepts in Thermal Physics (2nd Edition), by S.J. Blundell and K.M. Blundell (Oxford University Press, ISBN 9780199562107, paperback edition)
Aanbevolen materiaal
-
BOEKQuantum Mechanics: Pearson New International Edition by D. H. McIntyre, C. A. Manogue and J. Tate ISBN-10: 1292020830 • ISBN-13: 9781292020839
Coördinator
| dr. F.M. Freire | F.Freire@uu.nl |
Docenten
| dr. F.M. Freire | F.Freire@uu.nl |
| prof. dr. P. van der Straten | p.vanderstraten@uu.nl |
Inschrijving
Let op: deze cursus is niet toegankelijk voor studenten van andere faculteiten, bijvakkers mogen zich dus niet inschrijven.
Naar OSIRIS-inschrijvingen
Permanente link naar de cursuspagina
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