Quantum Mechanic : The Intro

If the above picture is your idea of an atom, with electrons looping around the nucleus, you are about 70 years out of date. It's time to open your eyes to the modern world of quantum mechanics! The picture below shows some plots of where you would most likely find an electron in a hydrogen atom (the nucleus is at the center of each plot).

What is quantum mechanics?

Simply put, quantum mechanics is the study of matter and radiation at an atomic level.

Why was quantum mechanics developed?

In the early 20th century some experiments produced results which could not be explained by classical physics (the science developed by Galileo Galilei, Isaac Newton, etc.). For instance, it was well known that electrons orbited the nucleus of an atom. However, if they did so in a manner which resembled the planets orbiting the sun, classical physics predicted that the electrons would spiral in and crash into the nucleus within a fraction of a second. Obviously that doesn't happen, or life as we know it would not exist. (Chemistry depends upon the interaction of the electrons in atoms, and life depends upon chemistry). That incorrect prediction, along with some other experiments that classical physics could not explain, showed scientists that something new was needed to explain science at the atomic level.

 If classical physics is wrong, why do we still use it?

Classical physics is a flawed theory, but it is only dramatically flawed when dealing with the very small (atomic size, where quantum mechanics is used) or the very fast (near the speed of light, where relativity takes over). For everyday things, which are much larger than atoms and much slower than the speed of light, classical physics does an excellent job. Plus, it is much easier to use than either quantum mechanics or relativity (each of which require an extensive amount of math).

 What is the importance of quantum mechanics?

The following are among the most important things which quantum mechanics can describe while classical physics cannot:

• Discreteness of energy


• The wave-particle duality of light and matter


• Quantum tunneling


• The Heisenberg uncertainty principle


• Spin of a particle

Discreteness of energy

If you look at the spectrum of light emitted by energetic atoms (such as the orange-yellow light from sodium vapor street lights, or the blue-white light from mercury vapor lamps) you will notice that it is composed of individual lines of different colors. These lines represent the discrete energy levels of the electrons in those excited atoms. When an electron in a high energy state jumps down to a lower one, the atom emits a photon of light which corresponds to the exact energy difference of those two levels (conservation of energy). The bigger the energy difference, the more energetic the photon will be, and the closer its color will be to the violet end of the spectrum. If electrons were not restricted to discrete energy levels, the spectrum from an excited atom would be a continuous spread of colors from red to violet with no individual lines.

 

The concept of discrete energy levels can be demonstrated with a 3-way light bulb. A 40/75/115 watt bulb can only shine light at those three wattage's, and when you switch from one setting to the next, the power immediately jumps to the new setting instead of just gradually increasing.

It is the fact that electrons can only exist at discrete energy levels which prevents them from spiraling into the nucleus, as classical physics predicts. And it is this quantization of energy, along with some other atomic properties that are quantized, which gives quantum mechanics its name.

 The wave-particle duality of light and matter

In 1690 Christiaan Huygens theorized that light was composed of waves, while in 1704 Isaac Newton explained that light was made of tiny particles. Experiments supported each of their theories. However, neither a completely-particle theory nor a completely-wave theory could explain all of the phenomena associated with light! So scientists began to think of light as both a particle and a wave. In 1923 Louis de Broglie hypothesized that a material particle could also exhibit wavelike properties, and in 1927 it was shown (by Davisson and Germer) that electrons can indeed behave like waves.

How can something be both a particle and a wave at the same time? For one thing, it is incorrect to think of light as a stream of particles moving up and down in a wavelike manner. Actually, light and matter exist as particles; what behaves like a wave is the probability of where that particle will be. The reason light sometimes appears to act as a wave is because we are noticing the accumulation of many of the light particles distributed over the probabilities of where each particle could be.

For instance, suppose we had a dart-throwing machine that had a 5% chance of hitting the bulls-eye and a 95% chance of hitting the outer ring and no chance of hitting any other place on the dart board. Now, suppose we let the machine throw 100 darts, keeping all of them stuck in the board. We can see each individual dart (so we know they behave like a particle) but we can also see a pattern on the board of a large ring of darts surrounding a small cluster in the middle. This pattern is the accumulation of the individual darts over the probabilities of where each dart could have landed, and represents the 'wavelike' behavior of the darts. Get it?

 Quantum tunneling

This is one of the most interesting phenomena to arise from quantum mechanics; without it computer chips would not exist, and a 'personal' computer would probably take up an entire room. As stated above, a wave determines the probability of where a particle will be. When that probability wave encounters an energy barrier most of the wave will be reflected back, but a small portion of it will 'leak' into the barrier. If the barrier is small enough, the wave that leaked through will continue on the other side of it. Even though the particle doesn't have enough energy to get over the barrier, there is still a small probability that it can 'tunnel' through it!

Let's say you are throwing a rubber ball against a wall. You know you don't have enough energy to throw it through the wall, so you always expect it to bounce back. Quantum mechanics, however, says that there is a small probability that the ball could go right through the wall (without damaging the wall) and continue its flight on the other side! With something as large as a rubber ball, though, that probability is so small that you could throw the ball for billions of years and never see it go through the wall. But with something as tiny as an electron, tunneling is an everyday occurrence.

On the flip side of tunneling, when a particle encounters a drop in energy there is a small probability that it will be reflected. In other words, if you were rolling a marble off a flat level table, there is a small chance that when the marble reached the edge it would bounce back instead of dropping to the floor! Again, for something as large as a marble you'll probably never see something like that happen, but for photons (the massless particles of light) it is a very real occurrence.

 The Heisenberg uncertainty principle

People are familiar with measuring things in the macroscopic world around them. Someone pulls out a tape measure and determines the length of a table. A state trooper aims his radar gun at a car and knows what direction the car is traveling, as well as how fast. They get the information they want and don't worry whether the measurement itself has changed what they were measuring. After all, what would be the sense in determining that a table is 80 cm long if the very act of measuring it changed its length!

At the atomic scale of quantum mechanics, however, measurement becomes a very delicate process. Let's say you want to find out where an electron is and where it is going (that trooper has a feeling that any electron he catches will be going faster than the local speed limit). How would you do it? Get a super high powered magnifier and look for it? The very act of looking depends upon light, which is made of photons, and these photons could have enough momentum that once they hit the electron they would change its course! It's like rolling the cue ball across a billiard table and trying to discover where it is going by bouncing the 8-ball off of it; by making the measurement with the 8-ball you have certainly altered the course of the cue ball. You may have discovered where the cue ball was, but now have no idea of where it is going (because you were measuring with the 8-ball instead of actually looking at the table).