Transcription of qitd114 Hilbert Space Quantum Mechanics
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qitd114 Hilbert Space Quantum Mechanics
qitd114 Hilbert Space Quantum MechanicsRobert B. GriffithsVersion of 16 January 2014 Contents1 Hilbert Space .. Qubit .. Intuitive picture .. Generald.. Kets as physical properties .. 42 Definition .. Dyads and completeness .. Matrices .. Dagger or adjoint .. Normal operators .. Hermitian operators .. Projectors .. Positive operators .. Unitary operators .. 93 Bloch sphere104 Composite systems and tensor Definition .. Product and entangled states .. Operators on tensor products .. Example of two qubits .. Multiple systems. Identical particles .. 13 References:CQT =Consistent Quantum Theoryby Griffiths (Cambridge, 2002), Ch. 2; Ch. 3; Ch. 4 except forSec. ; Ch. = Quantum Computation and Quantum Informationby Nielsen and Chuang (Cambridge, 2000).Secs. , ; through ; Hilbert Space In Quantum Mechanics the state of a physical system is represented by a vector in aHilbert Space : acomplex vector Space with an inner product.
⋆ In quantum mechanics a two-dimensional complex Hilbert space H is used for describing the angular momentum or “spin” of a spin-half particle (electron, proton, neutron, silver atom), which then provides a physical representation of a qubit. The polarization of a photon (particle of light) is also described by d= 2, so represents a qubit.
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