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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.

momentum vector pointing in a random direction in space, but subject to the constraint that a particular component of the angular momentum, say S z , is positive, rather than negative. • Thus in the case of |0i, which means S z = +1/2, think of S x and S y as having random values.

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