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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.

1.1 Hilbert space ⋆ In quantum mechanics the state of a physical system is represented by a vector in a Hilbert space: a complex vector space with an inner product. The term “Hilbert space” is often reserved for an infinite-dimensional inner product space having the property that it is complete or closed.

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