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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.
(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
We have seen that both the Schrödinger and the Heisenberg equation follows from Von Neumann’s Hilbert space formalism of quantum mechanics. Consequently, we have proved that this formalism properly unifies both Schrödingers wave mechanics, and Heisenberg, Born, and Jordans matrix mechanics.
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.
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 Heisenberg equation is commonly applied to a particle in an arbitrary potential. Consider a particle with an arbitrary one-dimensional potential \[H = \frac {p^{2}} {2 m} + V (x) \label{2.86}\]
After Schrödinger had shown the mathematical equivalence of wave mechanics, which he had discovered, with quantum mechanics, the fruitful combination of these two different areas of physical ideas resulted in an extraordinary broadening and enrich-ment of the formalism of the quantum theory.
