Hjem

1 Newtonian Mechanics
1.1 Classical space-time
1.2 The Galilean principle of relativity and inertial systems
1.3 Newton's laws of motion
1.4 Conservative force fields
1.5 Configuration space, phase space and state space
1.6 Digression: Exact and closed diferentials

2 Lagrangian Mechanics
2.1 Calculus of variations
2.2 The Euler-Lagrange equations
2.3 Change of variables
2.4 Hamilton's principle
2.5 Noether's Theorem
2.6 Constrained motion
2.7 Appendix

3 Hamiltonian Mechanics
3.1 Convex functions
3.2 Legendre transformation
3.3 Hamilton's equations
3.4 Some applications of Hamilton's equations
3.5 Legendre transform in thermodynamics

4 Hilbert Spaces
4.1 Inner product spaces
4.2 Orthogonality
4.3 Continuity of the inner product
4.4 Hilbert spaces and orthonormal bases
4.5 Orthonormal expansions
4.6 Fourier series

5 Operators on Hilbert spaces
5.1 Operators on finite dimensional real Hilbert spaces
5.2 Operators on finite dimensional complex Hilbert spaces
5.3 Operators on infinite dimensional Hilbert spaces
5.4 Diagonalisable operators and self-adjoint operators
5.5 The Fourier transformation as a unitary operator

6 Quantum mechanics
6.1 The quantum mechanical formalism
6.2 Transformations and symmetries in Quantum Mechanics
6.3 The momentum representation
6.4 Galilei invariance in Quantum Mechanics
6.5 The free particle
6.6 The free particle on a circle
6.7 The harmonic oscillator
6.8 Stability and the hydrogen atom

Index