Background in waves required for quantum mechanics

[QMechanic]

Hi,

I would appreciate suggestion which chapters from French's "Waves and Vibrations" (https://www.amazon.com/dp/8123909144/?tag=pfamazon01-20) and Norton's "Optics" (https://www.amazon.com/dp/0805385665/?tag=pfamazon01-20) need to be done to understand introductory quantum mechanics, especially those that assume basic understanding of physics and differential equations seen in waves and optics. Thanks.

 

[bhobba]

IMHO linear algebra is much more important.

Thanks
Bill

 

[QMechanic]

I have done the elementary linear algebra, right now looking to learn some more about waves and oscillations.

 

[bhobba]

I have done the elementary linear algebra, right now looking to learn some more about waves and oscillations.

That's great - but I am not sure that's really required for QM.

Linear algebra, and its more advanced incarnation in the form of Hilbert spaces is what's required for QM.

If you want to get a leg up learn the Dirac notation:
http://www.physics.umd.edu/courses/Phys374/fall04/files/DiracNotation.pdf

You may think its really important because you have come across things like the wave-particle duality etc - but really that's basically a crock - it's got nothing to do with it.

Thanks
Bill

 

[QMechanic]

Thanks for the link.

The complementary modern physics book I will use in my course suggests getting familiar with continuum mechanics before looking into Schrödinger equation and I have struggled to understand a bit the background on it provided there since the book is just an mathematical extension and does not provide much detail. Especially I need more material on D'Alembert's solution, differential wave equation for the string and Helmholtz equation which I thought I would find in any good waves book.

 

[bhobba]

Especially I need more material on D'Alembert's solution, differential wave equation for the string and Helmholtz equation which I thought I would find in any good waves book.

What you really need is a course on PDE's.

Don't worry - beginning books in QM provide all you need to know about that.

More advanced books - not so much - and a separate course in PDE's would be of value for that.

That said my background is applied math, not physics, and we tend to do the math before using it, but physics guys often do it as they go along.

I started doing a Masters in Applied Math and my advisor said since I had done a course on PDE's undegrad, guys with a similar background he had do a basic QM course were bored - it was basically just a course in Linear Algebra and PDE's for them - he now started them on intermediate QM.

Thanks
Bill

 

[QMechanic]

In case I want to get an early start on PDEs or look up references, would you recommend any easily accessible resource? Thanks.

 

[bhobba]

Sure thing.

Schaum's outline book is cheap and good:
https://www.amazon.com/dp/0071756183/?tag=pfamazon01-20

MIT's lectures look good as well:
http://ocw.mit.edu/courses/mathemat...fferential-equations-fall-2011/lecture-notes/

It examines Schroedinger's equation, which is one of the key equations in QM. That's why once you have come to grips with PDE's in a general sense QM becomes quite a bit easier.

Also, not just for PDE's, but for applied math in general, coming to grips with Distribution theory will be a great help:
https://www.amazon.com/dp/0521558905/?tag=pfamazon01-20

You will be entering the world of that damnable Dirac Delta Function and Fourier Analysis. You need it to understand that weird function, and distribution theory's treatment of the Fourier Transform and Series is just so simple and elegant - you won't want to do it any other way.

Thanks
Bill

 

[atyy]

I'd master French and Taylor, then pick up single slit diffraction, including Fraunhofer and Fresnel treatments, and the double slit (which is a special case of the single slit). The important ideas in French and Taylor are the special case of linear waves (I think that's all they do), superposition, normal modes (eigenvectors) from boundary conditions, Fourier series and transform, and the separation of variables.

One free resource that is good is Richard Ftzpatrick's http://farside.ph.utexas.edu/teaching/315/315.html, which starts with roughly the same material as French and Taylor, and ends at very introductory quantum mechanics (for the purpose of quantum mechanics, you can skip the chapter on dispersive waves). After that, Braam Gaasbeek has a good free introduction to quantum mechanics http://arxiv.org/abs/1007.4184, which takes over from where Fitzpatrick leaves off and gets to (almost) all of quantum mechanics in section 4.3.2.

For the gap in Gaasbeek's postulates of quantum mechanics, one can use http://arxiv.org/abs/1110.6815 , http://arxiv.org/abs/0810.3536 , http://arxiv.org/abs/0706.3526 . But I wouldn't worry about these until much later, since Gaasbeek's postulates are pretty much the same as Landau and Lishitz, Shankar, Sakurai and Napoltano, and Weinberg, which are all good and standard texts.

 

[QMechanic]

Oh, one more question while I am at it, what tool would you guys recommend for integration? My calculator does not have CAS so I tried using MATLAB but I think there might be better programs, can you think of any?

 

[atyy]

I learned QM in ancient days where in which the instructor said you only need to know one intergral: the Gaussian integral. After that everything is saddlepoint approximation. He was kidding, but it's not far from the truth.
http://www.umich.edu/~chem461/Gaussian Integrals.pdf
http://www.math.uconn.edu/~kconrad/blurbs/analysis/gaussianintegral.pdf

Have you tried http://www.wolframalpha.com/calculators/integral-calculator/?

 

[bhobba]

For the gap in Gaasbeek's postulates of quantum mechanics, one can use http://arxiv.org/abs/1110.6815 , http://arxiv.org/abs/0810.3536 , http://arxiv.org/abs/0706.3526 . But I wouldn't worry about these until much later, since Gaasbeek's postulates are pretty much the same as Landau and Lishitz, Shankar, Sakurai and Napoltano, and Weinberg, which are all good and standard texts.

I fully concur with that.

Starting out don't worry too much about foundational issues in QM.

Put them aside to begin with and delve into it via more advanced texts like Atty mentions, later.

I personally prefer Ballentine for that, and many who post here say its THE book:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

Atty is the odd man out.

However any of the books he mentions are VERY good and will serve the purpose of fixing up loose ends of beginner treatments.

You can also post here.

Thanks
Bill

 

[QMechanic]

Atty, I have haha, I just wondered if there is any tool that stands out and is used by most mathematicians and physicists.

 

[bhobba]

Oh, one more question while I am at it, what tool would you guys recommend for integration? My calculator does not have CAS so I tried using MATLAB but I think there might be better programs, can you think of any?

MATLAB was standard at my school.

But like I say it was the applied math department - don't know what the physics department used.

Actually there's something in the back of my mind that my advisor mentioned he now teaches the PDE course I did those many moons ago, and its a lot more using Matlab to solve the PDE rather than specific techniques like separation of variables these days - computers do the grunt work that used to torture math guys like me with long mind numbing manipulations.

Good riddance I say.

Thanks
Bill