- Title Pages
- Dedication
- Preface
- 1 Schrödinger equation on a lattice
- 2 Dirac notation
- 3 Back to the Schrödinger equation on a lattice
- 4 Operator mechanics
- 5 Time evolution and wavepackets
- 6 Simultaneous observables
- 7 Continuity equation and wavefunction properties
- 8 Bound states in one dimension
- 9 Scattering in one dimension
- 10 Periodic potentials
- 11 The harmonic oscillator
- 12 WKB approximation
- 13 Quantum mechanics and path integrals
- 14 Applications of path integrals
- 15 Angular momentum
- 16 Bound states in spherically symmetric potentials
- 17 The hydrogen-like atom
- 18 Angular momentum and spherical symmetry
- 19 Scattering in three dimensions
- 20 Time-independent perturbation expansion
- 21 Applications of perturbation theory
- 22 Time-dependent Hamiltonian
- 23 Spin angular momentum
- 24 Adding angular momenta
- 25 Identical particles
- 26 Elementary atomic physics
- 27 Molecules
- 28 The elasticity field
- 29 Quantization of the free electromagnetic field
- 30 Interaction of radiation with charged particles
- 31 Elementary relativistic quantum mechanics
- Appendix A Review of the Dirac delta function
- Appendix B Normalization integral of spherical harmonics
- Appendix C Legendre equation
- Appendix D Expression for the spherical Bessel function
- Index

# Continuity equation and wavefunction properties

# Continuity equation and wavefunction properties

- Chapter:
- 7 Continuity equation and wavefunction properties
- Source:
- Practical Quantum Mechanics
- Author(s):
### Efstratios Manousakis

- Publisher:
- Oxford University Press

This chapter discusses the continuity equation and continuity properties of the wavefunction and its spatial derivatives. In addition, it discusses other theorems which are useful for calculations, such as the variational theorem.

*Keywords:*
continuity equation, variational theorem, energy bounds, wavefunction conditions

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- Title Pages
- Dedication
- Preface
- 1 Schrödinger equation on a lattice
- 2 Dirac notation
- 3 Back to the Schrödinger equation on a lattice
- 4 Operator mechanics
- 5 Time evolution and wavepackets
- 6 Simultaneous observables
- 7 Continuity equation and wavefunction properties
- 8 Bound states in one dimension
- 9 Scattering in one dimension
- 10 Periodic potentials
- 11 The harmonic oscillator
- 12 WKB approximation
- 13 Quantum mechanics and path integrals
- 14 Applications of path integrals
- 15 Angular momentum
- 16 Bound states in spherically symmetric potentials
- 17 The hydrogen-like atom
- 18 Angular momentum and spherical symmetry
- 19 Scattering in three dimensions
- 20 Time-independent perturbation expansion
- 21 Applications of perturbation theory
- 22 Time-dependent Hamiltonian
- 23 Spin angular momentum
- 24 Adding angular momenta
- 25 Identical particles
- 26 Elementary atomic physics
- 27 Molecules
- 28 The elasticity field
- 29 Quantization of the free electromagnetic field
- 30 Interaction of radiation with charged particles
- 31 Elementary relativistic quantum mechanics
- Appendix A Review of the Dirac delta function
- Appendix B Normalization integral of spherical harmonics
- Appendix C Legendre equation
- Appendix D Expression for the spherical Bessel function
- Index