UCSCIPHY257.5 ECTSEnglishBachelor
Statistical Mechanics and Foundations of Quantum Mechanics
Faculteit—
NiveauBachelor
Studiejaar2026-2027
Beschrijving
Course goals
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 |
Content
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..
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