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6.1 The Schrödinger Wave Equation. There are several formalisms available to the quantum physicists. As stated in the previous chapter, the two original and independent formulations were those of Heisenberg and Schrödinger.
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.
Time-independent Schrödinger equation Let's apply the ideas of eigenfunctions to the time-dependent Schrödinger equation to extract the time-independent Schrödinger equation.
The Schrödinger Equation and its Interpretation. In this lecture you will learn: Schrödinger equation: the time-dependent form. Schrödinger equation: the probabilistic interpretation. Breakdown of determinism in quantum physics. The Quantum Physics of Photons.
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)
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
1925 (Heisenberg): Werner Heisenberg formulated a version of quantum mechanics that made use of matrix mechanics. We won’t deal with this matrix formulation (it’s rather di–cult), but instead with the following wave formulation due to Schrodinger (this is a waves book, after all).
