To the Stu­dent

This is a book on the real quan­tum me­chan­ics. On quan­tum scales it be­comes clear that clas­si­cal physics is sim­ply wrong. It is quan­tum me­chan­ics that de­scribes how na­ture truly be­haves; clas­si­cal physics is just a sim­plis­tic ap­prox­i­ma­tion of it that can be used for some com­pu­ta­tions de­scrib­ing macro­scopic sys­tems. And not too many of those, ei­ther.

Here you will find the same story as physi­cists tell their own stu­dents. The dif­fer­ence is that this book is de­signed to be much eas­ier to read and un­der­stand than com­pa­ra­ble texts. Quan­tum me­chan­ics is in­her­ently math­e­mat­i­cal, and this book ex­plains it fully. But the math­e­mat­ics is only cov­ered to the ex­tent that it pro­vides in­sight in quan­tum me­chan­ics. This is not a book for de­vel­op­ing your skills in clever math­e­mat­i­cal ma­nip­u­la­tions that have ab­solutely noth­ing to do with phys­i­cal un­der­stand­ing. You can find many other texts like that al­ready, if that is your goal.

The book was pri­mar­ily writ­ten for en­gi­neer­ing grad­u­ate stu­dents who find them­selves caught up in nano tech­nol­ogy. It is a sim­ple fact that the typ­i­cal en­gi­neer­ing ed­u­ca­tion does not pro­vide any­where close to the amount of physics you will need to make sense out of the lit­er­a­ture of your field. You can start from scratch as an un­der­grad­u­ate in the physics de­part­ment, or you can read this book.

The first part of this book pro­vides a solid in­tro­duc­tion to clas­si­cal (i.e. non­rel­a­tivis­tic) quan­tum me­chan­ics. It is in­tended to ex­plain the ideas both rig­or­ously and clearly. It fol­lows a just-in-time learn­ing ap­proach. The math­e­mat­ics is fully ex­plained, but not em­pha­sized. The in­ten­tion is not to prac­tice clever math­e­mat­ics, but to un­der­stand quan­tum me­chan­ics. The cov­er­age is at the nor­mal cal­cu­lus and physics level of un­der­grad­u­ate en­gi­neer­ing stu­dents. If you did well in these courses, you should be able to un­der­stand the dis­cus­sion, as­sum­ing that you start read­ing from the be­gin­ning. In par­tic­u­lar, you sim­ply can­not skip the short first chap­ter. There are some hints in the no­ta­tions sec­tion, if you for­got some cal­cu­lus. If you for­got some physics, just don’t worry too much about it: quan­tum physics is so much dif­fer­ent that even the most ba­sic con­cepts need to be cov­ered from scratch.

What­ever you do, read all of chap­ters 2 and 3. That is the very lan­guage of quan­tum me­chan­ics. It will be hard to read the rest of the book if you do not know the lan­guage.

De­riva­tions are usu­ally banned to notes at the end of this book, in case you need them for one rea­son or the other. They cor­rect a con­sid­er­able num­ber of mis­takes that you will find in other books. No doubt they add a few new ones. Let me know and I will cor­rect them quickly; that is the ad­van­tage of a web book.

The sec­ond part of this book dis­cusses more ad­vanced top­ics. It starts with nu­mer­i­cal meth­ods, since en­gi­neer­ing grad­u­ate stu­dents are typ­i­cally sup­ported by a re­search grant, and the quicker you can pro­duce some re­sults, the bet­ter. A de­scrip­tion of den­sity func­tional the­ory is still miss­ing, un­for­tu­nately.

The re­main­ing chap­ters of the sec­ond part are in­tended to pro­vide a crash course on many top­ics that nano lit­er­a­ture would con­sider el­e­men­tary physics, but that no­body has ever told you about. Most of it is not re­ally part of what is nor­mally un­der­stood to be a quan­tum me­chan­ics course. Read­ing, reread­ing, and un­der­stand­ing it is highly rec­om­mended any­way.

The pur­pose is not just to pro­vide ba­sic lit­er­acy in those top­ics, al­though that is very im­por­tant. But the pur­pose is also ex­plain enough of their fun­da­men­tals, in terms that an en­gi­neer can un­der­stand, so that you can make sense of the lit­er­a­ture in those fields if you do need to know more than can be cov­ered here. Con­sider these chap­ters gate­ways into their topic ar­eas.

There is a fi­nal chap­ter in part II on how to in­ter­pret quan­tum me­chan­ics philo­soph­i­cally. Read it if you are in­ter­ested; it will prob­a­bly not help you do quan­tum me­chan­ics any bet­ter. But as a mat­ter of ba­sic lit­er­acy, it is good to know how truly weird quan­tum me­chan­ics re­ally is.

The usual Why this book? blah-blah can be found in a note at the back of this book, {N.1} A ver­sion his­tory is in note {N.2}.