This example nicely shows several things about quantum mechanics. First quantum mechanics is a statistical theory of measurement. You only get the SG results after many spins have been filtered. Second, Heisenberg’s uncertainty relations tell us that you cannot devise an experiment that will measure both the Z and X polarization simultaneously. You can do it for one, but not the other, and vice versa.Read More
The lectures will be recorded at the Indian Institute of Technology (IIT) Madras which is part of the NPTEL program. A major goal of NPTEL is to raise awareness and improve scientific and technological education throughout India by use of multimedia. I will be giving a series of lectures on basic spin theory for chemistry and physics undergraduate students who have a basis in quantum mechanics; know of spin and its importance; and want to go deeper.Read More
After rolling 2, 3, 4, 10 and Avogadro’s dice, as seen in the entries below, it becomes clear that the most random states (most number of ways of rolling a number) always dominate while those with fewer arrangements occur less frequently: 1 Entropy: Randomness by rolling two dice 2 Entropy: Randomness by rolling three dice 3 Entropy: Randomness by rolling four dice 4 Entropy: Randomness by rolling ten dice 5 Entropy: Randomness by rolling Avogadro’s dice In this final entry of randomness and entropy, the concept of an ensemble is discussed. We are using a die to represent a particle that has six states that come up randomly. Hence we have treated systems with 2, 3, 4, 10 and Avogadro’s constant (let’s use 1023) of particles (dice) and have shown that as the number increases, the total number of accessible states, is given by 6n. Clearly the number of states in Avogadro’s case is 61023 : an enormous number!! If you start to roll this many dice, every roll gives...Read More
With Avogadro’s number of dice, you can roll them as much as you want, and the chance that there is an outcome other than the one that corresponds to the position of the spike is so unlikely you can safely ignore them.Read More
Exam time is coming and we have 1,100 freshman chemists getting stressed and nervous, so this is for them.
You need “stress” in your live. No stress would mean you would stay in bed all day. Well I’m a chemistry prof and like physical chemistry, and not a psychologist, but over the years you get to know students worries.
There are two types of stress. There is bad stress (“I’m scared”, “I’m dumb” “It is too hard?”) and there is good stress (“Great day, gotta get up!”, “I really want to understand stuff” “I am looking forward to tonight, so got to look good.”)
Use the good stress.Read More
The basic idea is that a physical system has many different arrangements (states) of particles which are consistent with some macroscopic quantity, like the temperature. Boltzmann found that out of all possible ways those particles can be arranged, only those that are consistent with the actual temperature need be considered. The chance of any other arrangements is negligible in comparison. Rolling dice illustrates this nicely.Read More