Hamiltonian and lagrangian mechanics

[robertjford80]

i'm just ready to start QM and I looked at the text and I turned to Shro eq to see if I could understand it and they mentioned Hamiltonian operator. It looked like the book assumed knowledge of H and L mechanics. Do I need to know this stuff? I wasn't told by others that I needed this. I was told just know Calc, Linear Alg and Diff Eq and statistics and you'll be fine.

 

[espen180]

Calc, Linear Alg and Diff eqs are the math requirements. You don't HAVE to know hamiltonian mechanics to do QM, but it is very convenient.

I think most physics undergrads first hear about the Hamiltonian operator (and thus the Hamiltonian function) when doing QM.

Basically you need to know Hamiltonian mechanics to understand why quantum mechanics is formulated the way it is. You also need it when you want to quantize a classical system using the canonical quantization scheme.

 

[lsaldana]

Look at a copy of Shankar's Principles of Quantum Mechanics. He reviews Lagrangian/Hamiltonian mechanics in chapter 2 I believe and constantly discusses the connection between these subjects and QM throughout the book.

 

[spaghetti3451]

These days, undergrads learn about the basic ideas of QM w/o having been introduced to Lagrangian and Hamiltonian mechanics. Unless you get very pedantic and want to know the full meaning of the Hamiltonian operator and how this idea of the Hamiltonian was borrowed from classical mechanics into quantum mechanics, unless you want that level of rigour, you should be fine w/o knowing H and L mechanics. But, just to throw caution to the wind, learning the foundations of qm, i.e. the mathematical formulation of qm in all its generality requires the understanding of l and h mechanics, but you don't meet such courses until well into your third year at uk unis (if you studdy theo physics) or graduate courses in the states.

 

[Lavabug]

I had 2 full courses in Lagrangian/Hamiltonian mechanics before my first QM. Not necessary, but having taken them can give you a warm fuzzy feeling when you make the connection between all the Dirac notation jargon and classical mechanics with Ehrenfest's theorem, Hamilton's and Newton's equations for the expectation values of observables, the harmonic oscillator, etc.

In fact I believe you could tear through QM without knowing any general physics at all if your control of linear algebra and calculus + complex variables is impeccable.

 

[robertjford80]

ok, thanks for the advice. remember impeccable etymologically means without sin.