Feynman’s Derivation of the Schrödinger Equation

Actually both parts are a joke, but only if you don't look for it.

"A few days before Christmas, 1925, Schrodinger, a Viennese-born professor of physics at the University of Zurich, took off for a two-and-a-half-week vacation at a villa in the Swiss Alpine town of Arosa. Leaving his wife in Zurich, he took along de Broglie's thesis, an old Viennese girlfriend (whose identity remains a mystery) and two pearls. Placing a pearl in each ear to screen out any distracting noise, and the woman in bed for inspiration, Schrodinger set to work on wave mechanics. When he and the mystery lady emerged from the rigors of their holiday on Jan. 9, 1926, the great discovery was firmly in hand."

http://www.nytimes.com/1990/01/07/books/the-lone-ranger-of-q...

I think you're both right.

The grandparent post is right in the sense that reductionism always reduces, ultimately, to a guess (in this case, Lagrangian mechanics is the guess).

You're right, though, in that a basic framework can be established, using minimal assumptions and axioms, in which most of classical physics and even much of quantum physics can be derived via (mostly) rigorous mathematical arguments. But that framework itself is, at the end of the day, a guess. It's simply the best guess we have at the given moment in time that fits the evidence (e.g., by allowing us to derive from it known rules and patterns that past generations have verified fit the evidence).

> It's actually not true to say that Schrodinger's equation, or F=ma, cannot be derived.

I don't think I said it couldn't be derived. I said there wasn't a "fundamental reason why the Schrödinger equation is X". Using Lagrangians to derive it then begs the question "but why must electrons obey the Lagrangian?".

> This is because in order to derive something, you need to first start from a set of assumptions. You can pick any assumptions you want, that is your privilege, as it is mine. If you want F=ma to be an assumption, you can go on and derive things from that.

Well, F = ma was a bad example, I grant you. It's actually a definition of what a force is, nothing more. But it's relevant, because it has a similar purpose (except in a different field of physics). A better example of a fundamental law would be action-reaction or something.

But yes, you're free to pick any assumption you like. But if you assume X, which came about because of assumption Y, it shouldn't be a shock that X can be used to derive Y. At that moment, they are just different notations for the same assumption. You might argue (and hell, I might even agree) that Lagrangians are so much more mathematically pleasing, so make a better assumption. But that doesn't change the fact that you're dressing up assumption Y as assumption X.

> But truly, F=ma is not the most general assumption in theoretical physics.

> If you look in any decent book on classical mechanics, you will find that F=ma in fact is derived from a much more general principle, the Lagrangian.

The Lagrangian is great for solving many problems. But it is definitely not more general than Newtonian mechanics. It can't deal with friction, or quite a few other non-conservative forces. On the plus side, solving oscillating systems is much easier. And it's so much nicer when not using Cartesian coordinates.

> That is the same Lagrangian that is the subject of the OP, which is used to derive the Schrodinger equation; and it's not just a coincidence.

While this is correct, Lagrangian mechanics refers to concepts such as energy which are defined from forces. In particular, Lagrangian's deal with systems with only conservative forces (but total energy may change with time). So it's really a circular argument to say "this concept can be derived from this even more abstract concept, which was actually defined from the first concept and at the end of the day is a guess."

There's nothing wrong with guessing fundamental laws. That's how the scientific method works, after all. You ask a question, guess the answer, predict what your guess would imply and test your predictions.

Shankar is all round a very practical book to pass quals, very poorly structured, highly pretentious by dealing with say parth integrals with grassman variables but doing an awful job at basic stuff such as adding angular momentum.

If you've got a math background I'd recommended you skip Shankar even more vehemently than I usually do.

I personally think that Shankar makes a great companion to Sakurai. Shankar is less rigorous but it explains things in a more accessible way which can be extremely helpful if you find Sakurai too terse on some topics.

It's been a long time now, but I pretty much agree with you. I really enjoyed Griffiths as an introduction but for reasons that escape me now I remember having a bad time with Shankar.

The QM class I originally took used Liboff. I could barely understand a word of it and ended up dropping the class. Later I found the Shankar book and was thrilled with it by comparison. I'm not a math whiz though, so lack of "rigor" on a first pass is just fine by me. For an intro level text for the average person, I found Shankar was one of the few accessible ones.

Haven't read Griffiths yet so I can't comment on it.

Griffiths is really great.

Personally I love Shankar, and can't stand griffiths.

What in the world are you talking about? Griffiths is substantially worse than shankar.

Griffiths doesn't even get into Hilbert spaces until chapter three, at which point he delivers a broken and incomprehensible explanation. He attempts to teach Hilbert operators by analogy to the multiplication or application by adjacency people use in normal arithmetic. This is a terrible approach, and confuses the hell out of students who haven't already taken abstract algebra.

In what way is Shankar less rigorous than Griffiths?

whoa.. I think we were literally in the same class at Lab. Nice to see you here!