Contents xi Problems try and statistics 47 es in Nature 6 es in quantum mechanics 5.2.1 The ground state and symmetry 49 5.2. Parity (P) 5.2.3 Time reversal 1 9 5.2.4 The galilean transformation 123 5.2.5 The Wigner-Eckart theorem 125 5.3 Identical particles:Bose-Einstein and Fermi-Dirac statis- tics 127 5.3.1 Identical bosons 130 5.3.2 Identical fe rmions and Pauli's exclusion principle Guide to the Supplements Problems 131 6 Three-dimensional problems 135 58 6.1 Simple three-dimensional systems 6.1.1 Reduced mass 135 6.1.2 Motion in a spherically symmetric potential 136 6.1.3 Spherical wat 6.Bound states in po 6.3 tentialels The three-dimen roge Supplement Numerical analyses 7Some fner pointsfq mechanics 7.1 at 4 Coordinate and momentum representations 7.2 s and operators 5 7.2.1 Bra and ket;abstract Hilbert space 7.3 Unbounded operators 7.3.1 Self-adjoint operators 8 7.4 Unitary transformations 7.5 The Heisenberg picture 169 7.5.1 The harmonic oscillator in the Heisenberg picture 1 7.6 The uncertainty principle 172 7.7 Mixed states and the density matrix 173 7.7.1 Photon polarization 7.8 Quantization in general coordinates 10 Further Supplements Problems 8 Path integrals Gre 183