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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.
Heisenberg, with help from Max Born and Pascual Jordan, came up with a matrix theory, which supposedly explained the travels of the electron by a complex form of mathematics called matrices. There remained some problems, however.
There are many good reasons to address the hydrogen atom beyond its historical signiflcance. Though hydrogen spectra motivated much of the early quantum theory, research involving the hydrogen remains at the cutting edge of science and technology.
(1) Schrödinger Picture: Everything we have done so far. Operators are stationary. Eigenvectors evolve under Ut(,t0). (2) Heisenberg Picture: Use unitary property of U to transform operators so they evolve in time. The wavefunction is stationary. This is a physically appealing picture, because
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)
5.1 The Schr¨odinger and Heisenberg pictures Until now we described the dynamics of quantum mechanics by looking at the time evolution of the state vectors. This approach to quantum dynamics is called the Schrodinger picture.
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.
