I What does it mean for a particle to vibrate?

[kipinaac]

I intuitively understand macroscopic vibration, but trying to understand what it means for a particle to vibrate doesn't seem to make sense from the classical understanding I have of momentum and energy. First, are particles even said to vibrate or have vibrational energy? If so, how is momentum conserved between finite intervals when, as I understand vibration, the particle could be moving in one direction at an initial time (t0) and the opposite at the final time (tf). In these cases I can see how energy, as a scalar, might be conserved, but not momentum as a vector.

For context, I'm trying to develop a deeper understanding of temperature and molecular walk, which depend on the random motion of a particle, which I vaguely understand as a store of "vibrational energy."

 

[Chandra Prayaga]

The random walk problem that you mentioned is not an example of vibrational energy but of kinetic energy of particles in random motion. By definition, a particle does not have an internal structure, so it does not vibrate.
Vibrational motion of a molecule is modeled by two (or more) particles interacting with each other through forces mimicked by springs.

 

[kipinaac]

The random walk problem that you mentioned is not an example of vibrational energy but of kinetic energy of particles in random motion. By definition, a particle does not have an internal structure, so it does not vibrate.
Vibrational motion of a molecule is modeled by two (or more) particles interacting with each other through forces mimicked by springs.

Then what exactly is meant by "random motion" and how does that not violate any conservation principles? My, again, classical understanding would have me believe a particle, unimpeded, will travel in a straight line.

Is the complex motion of a single particle in a large system of particles simply modeled as stochastic, or is there something fundamentally random about the motion of an individual particle?

 

[Chandra Prayaga]

Unimpeded is the correct word. Random motion does not occur in the case of a single particle. It happens in a gas at a finite temperature. The molecules or "particles" if you like, are in random motion, colliding with each other, and with the walls. The collisions result in random changes in directions of motion. This model is called the ideal gas model. All collisions are assumed to be elastic, and conserve both energy and momentum. You will find the model described in any introductory textbook of physics.

 

[kipinaac]

Unimpeded is the correct word. Random motion does not occur in the case of a single particle. It happens in a gas at a finite temperature. The molecules or "particles" if you like, are in random motion, colliding with each other, and with the walls. The collisions result in random changes in directions of motion. This model is called the ideal gas model. All collisions are assumed to be elastic, and conserve both energy and momentum. You will find the model described in any introductory textbook of physics.

I am definitely familiar with the ideal gas model. I have my copy of University Physics next to me. I just wanted to confirm that temperature/vibration are macroscopic quantities (describing systems of particles, rather than an individual particle).

 

[Chandra Prayaga]

Temperature is indeed a macroscopic concept. Vibration is not necessarily a "macroscopic" concept involving a very large number of particles. A single molecule with even two atoms (such as the hydrogen molecule) does oscillate.

 

[kipinaac]

Temperature is indeed a macroscopic concept. Vibration is not necessarily a "macroscopic" concept involving a very large number of particles. A single molecule with even two atoms (such as the hydrogen molecule) does oscillate.

Thanks for answering my questions! Clears some things up!