Principles and Definitions

If you have had Dr. Toggerson or Dr. Bourgeois for Physics 131, you are familiar with a distinction made between principles and definitions. The principles are the fundamental rules of the Universe that describe how things work. Concepts which are definitions, on the other hand, simply describe a quantity. For example,

is the definition of momentum for a massive particle; this equation offers no deep foundational insights into how the universe works. We physicists simply noted that the quantity came up a lot, and we gave it a name . In order to describe how the Universe works, principles often involve multiple definitions. Note that sometimes a principle or definition has an equation, while other times it is just stated in words! This point connects to Physics Goals 1 and 2 for this course.

To help acquaint those of you who may not be used to this distinction and to help organize the huge amount of factual information in this particular unit, I will list the principles for this unit. You can quickly see how short this list is.

Principles for This Unit

• “Waves are shy” – Quantum objects like light and electrons exist/propagate as waves. They only really behave in a particle-like manner when they interact/are observed.
• Since quantum objects exhibit both wave and particle properties, we need to be able to move back and forth between the two pictures – As you can see in the table below, both waves and particles have two independent properties. The goal is to move between them.
  

  Wave Properties		Particle Properties
  Amplitude		Probability of being at a location / Number of particles
  Wavelength		Momentum

• A confined wave must “fit in the box” – Thus, we must have an integer number of half-waves. For a nice symmetrical box, or box-like molecule, the wave will evenly fit in the box . However, even in situations such as atoms where the electron is more strongly attracted to the nucleus, we will have an integer number of half waves.
• Energy must be conserved

Other Basic Properties You Should Know

In chemistry, you probably saw the conversion between energy and wavelength for photons done through the equation . We will NOT consider that as a principle to begin analyses / solving problems. The reason is that, in chemistry, you only consider converting between energy and wavelength for photons. We want to think about BOTH photons AND electrons. It turns out that ONLY works for photons, while works for both photons and electrons! Thus, we consider to be our principle. Many students get tripped up by applying to electrons. Don’t fall into this trap!