Taking online courses

[Grinner]

Wanting to learn more about quantum physics, I'm thinking of taking an online course through Coursera. Presently, there are two options: "Exploring Quantum Physics (https://www.coursera.org/course/physicalchemistry)" and "Introduction to Physical Chemistry (https://www.coursera.org/course/physicalchemistry)", hereby known as EQP and PC respectively.

EQP actually started about a week-and-a-half ago, but judging from the syllabus, I might be able to catch up. On the other hand, it seems far more intensive, being focused solely on quantum physics. Frankly, it's a little intimidating, considering the degree of mathematics involved.

PC is split up into three segments, and the final one covers quantum physics*. This one seems a little more manageable, but I'm not entirely sure how greatly it differs from EQP. Additionally, the other two topics, thermodynamics and chemical kinetics, would be nice, but they don't seem that relevant to my goal.

Altogether, I'm really just looking for input, period. I'm kinda out my depth here.

*It's actually called quantum chemistry. What is that, anyway? How do you perform chemistry on a subatomic level?


Lecture 1: Introduction to quantum mechanics. Early experiments. Plane waves and wave-packets
Lecture 2: Interpretation and foundational principles of quantum mechanics
Lecture 3: Feynman formulation of quantum theory.
Lecture 4: Using Feynman path integral. Quantum-to-classical correspondence
Lecture 5: Back to the Schrödinger picture: bound states in quantum potential wells
Lecture 6: Cooper pairing in the theory of superconductivity
Lecture 7: Harmonic oscillator. Solution using creation and annihilation operators
Lecture 8: Classical and quantum crystals. Collective excitations in crystals - phonons
Lecture 9: Atomic spectra
Lecture 10: Quantum theory: old and new
Lecture 11: Solving the Schrödinger equation
Lecture 12: Angular momentum and the Runge-Lenz vector
Lecture 13: Electrical properties of matter
Lecture 14: Gauge potentials, spin and magnetism
Lecture 15: Quantum gases
Lecture 16: Topological states of quantum matter


Thermodynamics

Thermodynamic definitions
The zeroeth law of thermodynamics and temperature
The first law of thermodynamics and enthalpy
The second law of thermodynamics and entropy
The third law of thermodynamics and absolute entropy
Heat capacity
Reversible change
Hess’ Law
Gibbs energy and spontaneous change

Chemical Kinetics

Reaction rate
Effect of stoichiometry
Order of reaction
Half-life
Determining reaction order
Molecularity
The Arrhenius equation
Collsion theory
Transition state theory
Complex reactions
Rate-determining step
Steady state approximation

Quantum Chemistry

Introduction
Planck’s constant
The photoelectric effect
de Broglie’s particle waves
Heisenberg’s uncertainty principle
Schroedinger’s wave equation
The free particle
The particle in a box and application to linear polyenes
Hydrogenic atoms
Born’s interpretation of the wavefunction
Interpretation of radial and angular wavefunctions for hydrogenic atoms

[Larrx]

Typically I find prerequisites to be a better gauge of what a class will like than syllabus. Quantum can be covered in varying depth. I've taken three undergraduate courses that covered this material. The first was fairly gentle math-wise, but assumed a strong physics background. The second, which seems closest to the course you posted, required . . . all the math? It is very helpful to have a working knowledge of linear algebra, differential equations, and complex analysis at least before you dig into quantum mechanics in earnest.

Quantum theory has implications in chemistry. Most chemistry classes tend to discuss the results of quantum mechanics qualitatively and their effect on macroscopic systems. Just as interesting (imo) but requiring far less math.

[Grinner]

It is very helpful to have a working knowledge of linear algebra, differential equations, and complex analysis at least before you dig into quantum mechanics in earnest.

Geez. You weren't kidding, were you? :smalleek:

In the first lecture, after going through the history of quantum physics, the instructor constructs a rather intimidating equation, Schrodinger's equation, which purportedly describes a broad range of quantum effects*. Not only is it composed chiefly of variables and constants, but I also haven't a clue as to what most of them represent. Moreover, with no context as to how it describes everything from black body radiation to superconductivity, it seems, well, rather incredible. :smallconfused:

[Lokiare]

Geez. You weren't kidding, were you? :smalleek:

In the first lecture, after going through the history of quantum physics, the instructor constructs a rather intimidating equation, Schrodinger's equation, which purportedly describes a broad range of quantum effects*. Not only is it composed chiefly of variables and constants, but I also haven't a clue as to what most of them represent. Moreover, with no context as to how it describes everything from black body radiation to superconductivity, it seems, well, rather incredible. :smallconfused:

The highest math class I've taken was 'Discrete Mathematics'. I've found when talking to people that know quantum physics that they generally try to confuse you in order to view them as superior rather than trying to teach you something new. This leads me to think quantum physics might be a bunch of smoke and mirrors and not real science.

For instance people try to explain that you can only measure the location or velocity of a quantum particle but not both. They try to make it sound metaphysical or something, when in actuality measuring one changes the value of the other. Its like trying to measure where a tennis ball is blindfolded by throwing a basketball at it and listening to the sound of where the ball you threw lands.

[Larrx]

The highest math class I've taken was 'Discrete Mathematics'. I've found when talking to people that know quantum physics that they generally try to confuse you in order to view them as superior rather than trying to teach you something new. This leads me to think quantum physics might be a bunch of smoke and mirrors and not real science.

For instance people try to explain that you can only measure the location or velocity of a quantum particle but not both. They try to make it sound metaphysical or something, when in actuality measuring one changes the value of the other. Its like trying to measure where a tennis ball is blindfolded by throwing a basketball at it and listening to the sound of where the ball you threw lands.

While this does happen (wikipedia, I'm looking at you), I've never seen this behavior from a professor. People that know quantum physics spent years developing a language with which to discuss it. Conversations with lay people on the subject can present a non-trivial challenge. I think it's a mistake to attribute failures of communication to self-aggrandizement. It's just . . . hard to talk about about.

To the OP, Schrodinger's equation is intimidating to everyone the first time you see it. Solving it for the Coulomb potential (hydrogen atom basically) alone can take months. One of the first things done in a typical course it to separate the time dependence. The math gets harder after that, so if you have trouble following that early piece it might be a sign that a different course would suit you better. That being said, the mathematical techniques used in quantum are arcane. Approximately nobody walks into quantum understanding Legendre polynomials for example. There will be times when you are completely lost. This is normal :)

[Palanan]

Just passing through to say that nothing in this conversation so far makes me regret having been an English major.

:smalltongue:

[Knaight]

Quantum theory has implications in chemistry. Most chemistry classes tend to discuss the results of quantum mechanics qualitatively and their effect on macroscopic systems. Just as interesting (imo) but requiring far less math.

Physical Chemistry is really, really math heavy (particularly the Quantum Chem parts). You've basically got to be extremely comfortable with integration over spherical coordinates using the Schrodinger wave equation going in with a solid background of statistics, and unsolvable problems involving very complex approximation tools* follow quickly.

*Starting with the awfulness that is permutation theory

[NichG]

When a professor presents the subject matter in a way to inspire awe like that it can unfortunately impede understanding. I remember the point at which I realized that the language of physics and equations isn't just a matter of being able to say things very precisely, but its also a matter of being able to leave large sets of things unsaid and only focus on the consequences of a specific subset of properties. A physics grad student wrote on the board as a sort of half-joke 'the equation for the universe is H psi = E psi'. I realized that while that may very well be true, it also doesn't actually say very much - its only marginally more informative than saying 'everything in the universe can be expressed as a mathematical function'.

What it comes down to is that the Schroedinger equation is a template of sorts. Its a way that you can construct quantum mechanical descriptions of things for which you understand the classical equivalents. If you know the Hamiltonian - the 'H' in that H psi = E psi - then you can construct a quantum mechanical version of that system. But constructing/specifying a particular Hamiltonian is where all the details are hidden.

So, what's the Hamiltonian? Well, one way to think about it is that the Hamiltonian is that it's just the total energy of the system, but that doesn't explain why the Schroedinger equation looks the way it does or why it works. The usual way you learn about it is to first learn the classical case. In classical mechanics, you can write down conservation laws - conservation of energy, momentum, etc - and use those to figure out the motion. If you take the time derivative of a conserved quantity like the total energy (Hamiltonian), total momentum, or angular momentum, then that time derivative must be zero (because otherwise the conserved quantity would change with time). This process gives you equations relating the degrees of freedom of the system, which allows you to calculate the dynamics.

(Incidentally, the reason you get multiple equations from one Hamiltonian rather than just one equation is that you can group the terms in such a way that each term must independently be zero.)

So anyhow, that (very briefly) explains why in classical mechanics the dynamics can be derived from a equation for the total energy of the system. The Schroedinger equation is the quantum mechanical extension of that idea, where rather than having single-valued variables (e.g. position, velocity), you have a wavefunction that encodes the distribution of those variables. This is still a bit non-trivial - there are a couple of different ways you could try to write down such a system, and the quantum mechanical one isn't obvious - but that gets much deeper into things; suffice to say, the classical equivalent of writing a probability distribution and its equation of motion gives you something called the 'Master Equation for the probability' which looks like diffusion, but doesn't explain the results of experiments that led to the discovery of QM.

The most significant such result is a matter of debate of course, but the stability of atomic orbitals is at least a good way to understand why the Schroedinger's Equation does something non-trivial. If the processes involved were classical (e.g. diffusion-like) then you'd have a continuous set of states all the way down to collapse into the nucleus, because diffusion processes give rise to exponential functions, which have no periodicity. When you go to a wave-like description, the argument of the exponential goes imaginary and you get things with a given spatial periodicity. That periodicity means that you get a discrete set of states which satisfy the boundary conditions of the system - that gives you stable ground state orbits (you can't fit anything with a longer wavelength around the nucleus, and going to a shorter wavelength would actually increase the energy), discrete energy levels (and sharp spectral lines in absorption/emission spectra), etc.

Anyhow, hope this helps somewhat.

[Grinner]

Finished the second lecture. The subject seemed to be probability insofar as locating particles is concerned. I'm still not entirely sure how that's supposed to work, given that the accuracy of different instruments is going to vary, but I'm starting to see some recurring patterns in the math. I still haven't a chance of actually completing the homework, but I'm proud of what I can comprehend.


For instance people try to explain that you can only measure the location or velocity of a quantum particle but not both. They try to make it sound metaphysical or something, when in actuality measuring one changes the value of the other. Its like trying to measure where a tennis ball is blindfolded by throwing a basketball at it and listening to the sound of where the ball you threw lands.

A most illustrative example. Thanks! :smallsmile:


The math gets harder after that, so if you have trouble following that early piece it might be a sign that a different course would suit you better.

Oh, no. I'm afraid my mathematical incompetence is a foregone conclusion.

That, of course, will not stop me from at least trying.


Anyhow, hope this helps somewhat.

In broad strokes, I think I understand what you're saying. The specific details elude me, however.

I find it interesting that, like "H psi = E psi", many of the expressions in the lectures seem to be restatements of other expressions.

[DodgerH2O]

I can't imagine that the material in Physical Chemistry will help you understand Quantum Mechanics all that much unless you already have a background in both Physics and Chemistry. Most of it is material covered in other classes but applied specifically to chemical structures and interactions. I would stick with the EQP if your goal is specifically learning about QM stuff. I mean I found PChem's implications fascinating but mostly it was math. Lots and lots of math.

[gomipile]

I have two book recommendations for you, both of which can help develop intuition for quantum mechanics.

The first, which you should definitely read and has practically no prerequisites, is QED by Richard Feynman. His explanations help a ton with intuition, and when you learn the math behind what he says in this book somewhere else, it should all make a lot more sense than it would otherwise.

The second is a book which I consider to be one of the very best undergraduate-level introductions to the meat of nonrelativistic quantum mechanics. This is Primer of Quantum Mechanics by Marvin Chester. This book has very good intuitive explanations of the basics of QM, and uses the Dirac notation throughout, which makes it easier to get into some of the harder stuff later, since you won't be struggling with new formalism at the same time as new physical concepts. Chester's book doesn't shy away from math, so it's a good companion piece to any course in basic QM. Dover reprinted it in 2003, and you can get the hardcover used for about $11.