Before we go into that, though, it’s worth exploring Planck’s hypotheses and their implications a little bit further. As we will see over the course, blackbody radiation is not the only case where energies are restricted to certain, discrete levels. This concept shows up over and over again in the wacky world of quantum physics. In fact, it’s so important that physicists have given it a fancy name: quantization.
Moreover, whenever the energy levels of physical system are quantized, we say that there corresponds to each level a quantum state. Stated differently, whenever a system is in a particular quantum state, is has a specific, corresponding energy level. To put these important concepts into better perspective, let’s consider a few real-world examples.
DEFINITION
Energy quantization of a physical system implies that its energy levels are limited to certain discrete values.
Whenever a system’s energy corresponds to one of these particular energy levels, the system is in a corresponding quantum state.
The next time you get to watch a school band concert, take a close look at the trombone player. While playing, she’ll be moving the slide of her trombone out to certain positions corresponding to the musical notes that she is playing. Of course, we all know that if she wanted to, she could move the slide continuously along, and in the process hit not only all the standard notes but every possible pitch in between. A trombone, therefore, is capable of producing a continuous range of pitches. This is analogous to the continuous range of energies that classical physicists believed heated electrons could assume.
Next, take a look at the trumpet player. While he is playing, he’s holding down the valves of his trumpet in different combinations to hit the standard notes. Unlike the trombone player, though, he is not able to play the infinite number of pitches in between; he is limited to a finite set. Just like the allowed energies in Planck’s heated solid, the trumpet’s pitch is quantized.
QUANTUM LEAP
The “state” of an object includes all the information you need to explain how the laws of physics will affect it. As we’ll soon see, a quantum state is merely the quantum-physics extension of this concept. Just as before, if you know what quantum state an object is in, you have (in principle) all the information you need to deduce all of its physical properties.
America’s favorite pastime offers another illustration of quantization. When a baseball player is up to bat, his objective is to hit the ball and then run as far as he can around the bases. The further he gets, the better. But, it is only if he manages to travel all the way around and cross home plate that his team will register a run. The scoring of baseball is therefore quantized. Runs come only in whole numbers (also called integers). Even though most players would be happy with a triple, when all’s said and done, a triple is worth 0 runs, not 0.75.
An everyday, though artificial, analogy of quantum states can be given by a simple staircase. Each time you move up from one step to the next, you move just a tad further from Earth’s center. This means that you have a slightly higher gravitational potential energy when at each higher step. In some sense, then, your “energy levels” are quantized. This would imply that on every different step, you are in a different “quantum state.”
Be careful not to take this analogy too far, though. Your energy levels in this case are not “quantized” due to the effects of quantum physics. They were “quantized” by the carpenter who made them, and he could have made them practically any height he wanted. For this reason, you don’t truly move from one “quantum state” to the next when climbing up the steps.
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