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Schrödinger’s version of quantum mechanics is based on the evolution of a wave function characterizing the system, a notion previously introduced in Chapter 4, as dictated by the Schrödinger wave equation .
The Schrodinger equation: “norm”, “one particle” Important concept: the norm associates ψ(x,t) with “one particle” The association of “one particle” is associated with the “norm” of ψ(x,t). We require that ψ(x,t) be normalized so that: 1 = Z +∞ −∞ dxψ∗(x,t)ψ(x,t) . (5.31)
The Schrödinger equation is the heart of non-relativistic quantum me-chanics, in that virtually all the physics is derived from its solutions in var-ious systems. The origin of the equation is difficult to pin down, as every book on introductory quantum mechanics has its own way of introducing it.
Chapter 1. Wave mechanics and the Schr ̈odinger equation. William Thomson, 1st Baron. Although this lecture course will assume a familiarity with the basic concepts of wave mechanics, to introduce more advanced topics in quantum theory, it makes sense to begin with a concise review of the foundations of the subject.
In this section we’ll give a \derivation" of the Schrodinger equation. Our starting point will be the classical nonrelativistic expression for the energy of a particle, which is the sum of
For an operator A, ˆ if. ˆAf(x; A) = A · f(x; A) for a given A ∈ C, then f(x) is an eigenfunction of the operator A ˆ and A is the corre sponding eigenvalue. Operators act on eigenfunctions in a way identical to multiplying the eigenfunction by a constant number.
Schrödinger Equation: The Time-Independent Form In this lecture you will learn: • Schrödinger equation –the time-independent form • Particle in an infinite potential well • Quantum mechanical tunneling
