Background

The assumptions of Quantum Mechanics

The following module will discuss methods of solution for the expected position of an electron in a single-electron hydrogen atom.

In doing this, there will be some assumptions about the quantum world that may be hard to accept.

The first of these assumptions is that traditional understanding of the interaction and motion of particles of matter as opposed to waves are not sufficient to describe the quantum world. Through the diffraction and interference of light we see that light has properties of a wave. Its energy and momentum can be characterized by the frequency of that wave, and its intensity can be characterized by the amplitude of that wave. However, when we try to measure the absorption of light in very small quantities, such as is shown by the photoelectric effect, we see that light is always absorbed in discrete packets of energy. Light, it seems, has both a particle-like and wave like nature. It appears in many instances to exist as a particle but to interact like a wave. In addition, it has been seen that at appropriate energies, we can see the same thing with what we might term regular matter. The traditional evidence of this is electron diffraction, where the paths of electrons when scattered at high energies show interference patterns, as would a wave. Quantum particles, like light, show properties of both a particle and a wave, existing as a particle but interacting like a wave.

The second of these assumptions is that at the quantum level, we really cannot speak of what anything is until we make a measurement. In the macroscopic world, the interaction of light moving from a source to an object we are trying to observe, being absorbed or scattered, and if scattered proceeding on to our eyes for measurement does not significantly affect the bulk motion of say, a baseball, your car, or your computer screen. But if what you want to see is an atom, or an electron, or a proton, then the effect of a single photon or electron being used to try and probe for the particle will disturb the particle. Since all we can do then is to make a measurement by stopping or interfering with a quantum particle, until we make that measurement we can only speak of probabilities. This led to a schism in the physics world in the early-mid 1900's. Physicists were torn between two possibilities: (a) the quantum world essentially makes sense, but we have no ways of determining the underlying laws because we cannot measure the initial conditions without disturbing the system, or (b) nature exists simultaneously in a combination of infinite possibilities determined by a complex (i.e. containing real and imaginary components) wave function, and is only forced into one of those possibilities by the act of measurement. Faced with no experiment which could determine a difference between the two, and with greater progress at defining laws which seemed to govern a wave function which could describe on a statistical scale the quantum world, the latter choice, also known as the Copenhagen interpretation of quantum mechanics, eventually gained the most favor.