11. Written in Dirac notation as standard, the transformations on quantum state vectors are: 12. Anderson localization prevents the spread of quantum states in random media. 13. This quantum state can be represented as a span the space. 14. However, in analyzing quantum states and black holes, physicist black hole evaporates ". 15. Thus, a wavefunction describes the superposition of all quantum states of a particle. 16. In quantum mechanics, a particle is described by a quantum state . 17. In general, measuring an unknown quantum state changes that state in some way. 18. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state . 19. A make exact copies of a quantum state , this method does not work. 20. But orthogonal quantum states can always be distinguished via projective measurements.