How best to prepare for QM next semester.

[Bobbo Snap]

Greetings everyone,

This is my first post although I have referenced this site numerous times. It's a great resource, so many thanks to the admin and participants.

A little background:
I am in my junior year of a physics/mathematics double major at an unremarkable state university. The math/physics department at my school is combined and very small (we only have 8 or 9 tenured faculty) and the focus is strongly on mathematics. There are some very good math professors but physics is lacking I'm afraid. This is too bad because, although I'm a double major, my real interest is in physics. I took the double major because it only requires 3 or 4 more mathematics courses than what is already required for the physics major. So the situation is not ideal but, c'est la vie, I'm a non-traditional student and this university was my only option for my bachelors degree.

Now, I've held straight A's up until this point, but I've sort of hit a bump in the road. I didn't do as well as I would have liked in Theoretical (Classical) Mechanics last semester; grades are not finalized yet but I will most likely be getting a B in the class. There are many factors that contributed to this hiccup and I won't go into all of them. I will say that time and effort are not the problem. In the heat of the semester, I typically spend 70-80 hrs. a week on schoolwork (including attending class). If this isn't sufficient when taking 15 credit hours, there's nothing to be done I guess. I can't devote more time than that.

I think some of the problem is a lack of coordination between the math and physics faculty. I don't feel the prerequisite math courses prepare me well enough for the physics courses that use them. For instance, I've taken O.D.E., multivariable and vector calculus, and linear algebra and I did well in each class but I really struggled applying these concepts in Mechanics. The math courses definitely don't stress application but it could also be that I'm having a hard time bridging the gap. Either way, I want to do better next semester. The grades matter to me but it matters more that I really understand the material as I plan to go on to grad school.

So finally to the question. I'm taking Quantum Mechanics next semester (in about a month) and I want to be sure that I'm prepared. I had a brief intro to QM in the third semester of general physics but this is a full course and the instructor is demanding from what I hear. I'd appreciate any advice you can give on specific mathematics and general physics topics to brush up on. I have copy of "Mathematical Methods in the Physical Sciences" by Mary Boas that I plan on studying in the month before school starts up again. I've encountered most of the topics in it but I'm hoping it will help me better apply the math to physics. Are there any other good references you guys can recommend? I'm also open to suggestions on improving my study habits in order to learn material faster and better than I have been, thus far.

I may have left out pertinent info but I feel the post is long winded enough. Thanks in advance for all replies.

 

[Nabeshin]

I think some of the problem is a lack of coordination between the math and physics faculty. I don't feel the prerequisite math courses prepare me well enough for the physics courses that use them. For instance, I've taken O.D.E., multivariable and vector calculus, and linear algebra and I did well in each class but I really struggled applying these concepts in Mechanics. The math courses definitely don't stress application but it could also be that I'm having a hard time bridging the gap. Either way, I want to do better next semester. The grades matter to me but it matters more that I really understand the material as I plan to go on to grad school.

So finally to the question. I'm taking Quantum Mechanics next semester (in about a month) and I want to be sure that I'm prepared. I had a brief intro to QM in the third semester of general physics but this is a full course and the instructor is demanding from what I hear. I'd appreciate any advice you can give on specific mathematics and general physics topics to brush up on. I have copy of "Mathematical Methods in the Physical Sciences" by Mary Boas that I plan on studying in the month before school starts up again. I've encountered most of the topics in it but I'm hoping it will help me better apply the math to physics. Are there any other good references you guys can recommend? I'm also open to suggestions on improving my study habits in order to learn material faster and better than I have been, thus far.

My suggestion would be to really pay attention to the use of 'familiar' mathematics in physics classes. Obviously you know how to solve ODEs and PDEs in general, but you'll notice the technique from math classes doesn't match up to what's done in physics books. Often times in physics you just 'guess' the solution, since you have physical intuition for what the solution must be like. This is a recurring theme in the application of mathematics to physics, and if you look for it you'll see it all over the place.

As long as you have a grasp of linear algebra, the mathematics of QM is fine. The issues tend to be more conceptual.

Also, I obviously know nothing about your study habits but putting 70-80 hrs a week in seems like too much. This means you're spending 55-65 hrs a week on coursework? I can't really say more, but it certainly seems like this could be streamlined a lot...

 

[Bobbo Snap]

Also, I obviously know nothing about your study habits but putting 70-80 hrs a week in seems like too much. This means you're spending 55-65 hrs a week on coursework? I can't really say more, but it certainly seems like this could be streamlined a lot...

I definitely need to do something different here, I was quite burned out by the end of the semester. I was a bit overzealous taking some courses that were a over my head and they required a lot of self study. It's my junior year and the change to all upper division courses was more difficult than I anticipated too. I lightened my load a little bit next semester so hopefully it won't be as bad.

You mentioned P.D.E.'s which I haven't had a full course on yet, i suspect some review here may be helpful. I remember they appear in Schrödinger's Eqn. which we had to take on faith in Gen. Phys. 3...

Thanks for the advice BTW.

 

[vincent_vega]

you're probably fine I wouldn't worry too much. Any pdes you need are solved in griffiths (if that's the textbook you will be using). I'm almost done with QM right now, and all I did was review a little linear algebra. undergrad qm is pretty basic stuff

 

[marcusl]

I suggest that you study linear algebra, particularly eigen-values and -vectors, until you understand them well. Then study matrix methods and, again, how they are used in eigenvalue problems.

 

[ahsanxr]

You may find this thread useful:

https://www.physicsforums.com/showthread.php?p=4178358

 

[Bobbo Snap]

Thanks for the replies (and the link ahsanxr). I will brush up on my linear algebra. I have Poole's "Linear Algebra: A Modern Introduction" that we used in my linear course and Boas' "Mathematical Methods in the Physical Sciences" mentioned above. Does anybody have any opinions on these references? I wasn't overly impressed with Poole the first time through.