Development of Modern Quantum Mechanics
In 1925, building on de Broglie's hypothesis, Erwin Schrödinger developed the equation that describes the behaviour of a quantum mechanical wave. The equation, called the Schrödinger equation after its creator, is central to quantum mechanics, defines the permitted stationary states of a quantum system, and describes how the quantum state of a physical system changes in time. In the paper that introduced Schrödinger's cat, he says that the psi-function featured in his equation provides the "means for predicting probability of measurement results," and that it therefore provides "future expectation, somewhat as laid down in a catalog."
Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a classical wave, moving in a well of electrical potential created by the proton. This calculation accurately reproduced the energy levels of the Bohr model.
At a somewhat earlier time, Werner Heisenberg was trying to find an explanation for the intensities of the different lines in the hydrogen emission spectrum. By means of a series of mathematical analogies, Heisenberg wrote out the quantum mechanical analogue for the classical computation of intensities. Shortly afterwards, Heisenberg's colleague Max Born realised that Heisenberg's method of calculating the probabilities for transitions between the different energy levels could best be expressed by using the mathematical concept of matrices.
In May 1926, Schrödinger proved that Heisenberg's matrix mechanics and his own wave mechanics made the same predictions about the properties and behaviour of the electron; mathematically, the two theories were identical. Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg saw no problem in the theoretical prediction of instantaneous transitions of electrons between orbits in an atom, but Schrödinger hoped that a theory based on continuous wave-like properties could avoid what he called (in the words of Wilhelm Wien) "this nonsense about quantum jumps."
Read more about this topic: Introduction To Quantum Mechanics
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