The Old Quantum Theory

The New Quantum Mechanics
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That Old Quantum Theory

Einstein called these "light quanta. An electron in an atom could jump up from one fixed orbit to an orbit of higher energy, but only if it absorbed energy precisely equal to the difference of energy between the orbits. Likewise, an electron could jump down to an open lower-energy orbit by giving off energy precisely equal to the energy drop. These two events are the origins of the so-called absorption and emission spectra of the elements--their characteristic colors.

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The quantum behavior of electrons in atoms contradicted not only the "classical" mechanics of Sir Isaac Newton, but also the classical electromagnetic theory, which was developed in the nineteenth century and was spectacularly successful for describing light and radio waves. Even worse, while an electron orbited in a quantum energy state, it did not radiate away its energy as the electromagnetic theory required.

Energy Level Changes

The old quantum theory is a collection of results from the years – which predate modern quantum mechanics. The theory was never complete or. The Old Quantum Theory. A volume in The Commonwealth and International Library: Selected Readings in Physics. Book • Authors: D. TER HAAR.

Instead, as Bohr postulated but could not explain, each quantum orbit could be considered a "stationary state," with energy losses or gains occurring only when the electrons jumped between the stationary states. In , Sommerfeld enhanced the Bohr theory of the atom by introducing non-circular orbits, by allowing quantized orientations of the orbits in space, and by taking into account the relativistic variation in the mass of the electron as it orbited the nucleus at high speed. The Bohr-Sommerfeld quantum theory of the atom proved remarkably successful for the simplest case, a hydrogen atom one electron orbiting a nucleus.

Energy Levels

Difficulties began to arise, however, for more complicated atoms in the early s. Family Matters The Uncertainty Principle The Copenhagen Interpretation What I will do for the rest of this section is to discuss each of the founding fathers listed above and explain some of the basic concepts of their contributions. Let's begin with a little overview of just what quantum mechanics is all about. A quantum leap is a discontinuous transition between quantum states.

What this means is that an electron in one energy level in an atom jumps instantly into another energy level, emitting or absorbing energy as it does so. There is no in-between state, and it doesn't take any time for the leap to occur.

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The leaps also occur at random, selecting from the options available to the quantum entity in accordance with the strict rules of probability. So a quantum leap is a sudden change in a system that occurs on a very small scale and is made at random. What is quantum mechanics? Well, essentially it's the mechanics of quantized things. Okay, so what does that mean? In physics, mechanics is not about fixing your car, but is the explanation of the way things work in terms of energy, forces, and motion. And anything that is quantized is simply expressed in multiples of some small measurable unit.

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Let us now describe this. Einstein's other theories explained the equivalence of mass and energy, the particle-wave duality of photons, the equivalence principle, and special relativity. Julian Schwinger writes a paper proposing unification of weak and electromagnetic interactions. Applied as a model for the specific heat of solids, this resolved a discrepancy in pre-quantum thermodynamics that had troubled 19th-century scientists. Experiments verify that there are two distinct types of neutrinos electron and muon neutrinos. For instance, exactly where is a wave? And m is called the magnetic quantum number , because the z component of the angular momentum is the magnetic moment of the rotator along the z direction in the case where the particle at the end of the rotator is charged.

As you already know, before the turn of the century, the way things worked was explained by Newtonian mechanics or classical physics. And the central feature of Newtonian mechanics was that everything was continuous; things flowed smoothly through space; energy could come in an infinite range of amounts; light undulated in a continuous wave; there was no minimum amount of anything. Quantum mechanics changed all that. Now energy, light, force, and motion all came to be quantized. For something to be quantized, you can't have just any old amount; you can only have multiples of certain minimum quantities.

Quantum mechanics meant that all the qualities of subatomic things, and by extension, all things, were precisely quantifiable.

Quantum Mechanics

Nature revealed herself to be somewhat grainy or jerky, jumping from one quantum amount to the other, never traversing the area in between. This leads to an uneasy uncertainty about what is going on between those quantum states, or to put it into a popular phrase, quantum leaps. In fact, as it turns out, there is no way of knowing the exact state of things between quantum states. In our perception and that is a key ingredient , there is no transition between quantum states.

You can have one or two or three units of energy or momentum or light or force or matter or whatever, but there is no such thing as one and one-half or two and three-quarters units.

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An example of this might help you understand. Imagine that a child is jumping up the stairs.

Bohr's quantum theory revised

A quantum leap is the transition from one state to the next state, the same as a child jumping from the first stair to the second stair. Depending on the amount of energy she has, she can also jump up to the third stair, the fourth, or the sixth. But she can't jump in between the stairs and land safely.