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Pc2 l07 08

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CHEM F213 : Physical Chemistry-II Module-I: Development of Quantum Theory Postulates of quantum Mechanics: Wavefunction, Schrödinger equation (Lectures 07, 08) - Prashant Uday Manohar In this sub-module, we already learnt: • Wavefunction, Time-evolution, stationary states • Operators and eigenvalue equations • Linear operators, Hermitian operators, some theorems BITSPilani, Pilani Campus Postulate-I The sate of a quantum-mechanical system is completely specified by a wave-function Ψ(r1, r2,...rN,t) of the system and is the function of the position coordinates of all the particles; and of time. The wavefunction has important property that Ψ*Ψdτ ≡ Ψ*(r1, r2,...rN,t)Ψ(r1, r2,...rN,t)dx1dy1dz1...dxNdyNdzN is the probability that the system is found in the infinitesimal volume element, dτ located at (r1, r2,...rN) at the time, t. BITSPilani, Pilani Campus Postulate-II To every observable in classical mechanics, there corresponds an operator in quantum mechanics. More precisely: To every observable in classical mechanics, there corresponds a linear, Hermitian operator in quantum mechanics. BITSPilani, Pilani Campus Postulate-III In any measurement of the observable associated with the operator, A, the only values that will ever be observed are the eigen values a, which satisfy the eigenvalue equation: Af = a f The physical interpretation of this is, that, when we measure a physical property of a quantum mechanical system, the act of measurement takes ...
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