tag:blogger.com,1999:blog-393324845011978943.post5769333520815773459..comments2019-10-15T21:34:56.835-04:00Comments on Behind the Guesses: The Schrödinger Equation - CorrectionsEli Lanseyhttp://www.blogger.com/profile/01955234977479398457noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-393324845011978943.post-25127364063849909102010-09-22T04:35:46.587-04:002010-09-22T04:35:46.587-04:00Hello *,
I agree with Peeter, that all that is ni...Hello *,<br /><br />I agree with Peeter, that all that is nice relationship between CM and QM, but has methodically nothing to do with a derivation of the Schrödinger equation. One methodically correct ansatz is the question, how the mechanics of an oscillator looks like, if there are no turning points? This question is admissible within Euler's representation of CM, because the basic laws/principles do not require turning points. It cannot be answered within CM, hence, it transcends CM (cf Gödel's theorem).<br /><br />Best wishes,<br /><br />Peter<br />enders@dekasges.deAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-393324845011978943.post-25990884507961683372009-10-05T23:06:25.061-04:002009-10-05T23:06:25.061-04:00I think it is hard to answer a broad question like...I think it is hard to answer a broad question like the one posed without some idea of the starting point. I have an undergrad in engineering which provided good math fundamentals, but only basic physics. I'd rank my physics knowledge as perhaps (?) second year level undergrad physics so study of basic QM is timely (for me)<br /><br />My engineering program did include a small half semester course in QM basics, and this has helped as a base for further self study. That course used the MIT book by French, which has a number of admirable features for an introductory text.<br /><br />I've personally learned a lot from Bohm's book (Dover), which is cheap, and perhaps a bit old fashioned. It covers both motivational aspects and specifics with good depth. It has taken me a long time to work through that book (perhaps true of any QM text), and I am still not done.<br /><br />One resource that I particulariliy liked was Cathryn Carson's History 181B: Modern Physics, on iTunesU. She is an excellent and engaging lecturer, and builds up to Quantum field theory in a descriptive and highly accessable fashion, amazingly without requiring any mathematics (it's an arts course, not a physics nor engineering). I found this gave me an excellent high level picture of why quantum theory is worth studying and how it fits in with many other aspects of physics.Peeter Joothttps://www.blogger.com/profile/13747647271625793131noreply@blogger.comtag:blogger.com,1999:blog-393324845011978943.post-1545686097166127842009-10-05T20:31:54.677-04:002009-10-05T20:31:54.677-04:00Hi Anonymous,
I think you can learn the principles...Hi Anonymous,<br />I think you can learn the principles of QM by yourself. If you've never learned any of it before, I'd recommend starting with Griffiths' book. Peeter has taught himself most of this stuff, so you could probably ask him for advice, too.Eli Lanseyhttps://www.blogger.com/profile/01955234977479398457noreply@blogger.comtag:blogger.com,1999:blog-393324845011978943.post-39850729234615140972009-10-02T22:34:52.426-04:002009-10-02T22:34:52.426-04:00Hi Eli
I would like to thank you. I am a graduate ...Hi Eli<br />I would like to thank you. I am a graduate student. I would like to ask a question: Can I learn the principles of Quantum Mechanics by myself.<br />Thank you againAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-393324845011978943.post-36679417522646453862009-06-04T14:31:35.892-04:002009-06-04T14:31:35.892-04:00Okay, that makes sense. It never occured to me th...Okay, that makes sense. It never occured to me that there ought to also be a momentum representation of (18). I'll have to play around with that, but am guessing I have to dig up my mechanics book covering Hamiltonian x,p coordinate representation first.Peeter Joothttps://www.blogger.com/profile/13747647271625793131noreply@blogger.comtag:blogger.com,1999:blog-393324845011978943.post-44432206633463931502009-06-04T13:16:23.147-04:002009-06-04T13:16:23.147-04:00Peeter,
I actually think of eq. (16) as the S.E. ...Peeter,<br />I actually think of eq. (16) as the S.E. Each step afterwards assumes a particular representation of the equation. in this post I chose the more familiar position representation. As to why, in this representation the momentum operator is the differential operator - that is a topic for another post...Eli Lanseyhttps://www.blogger.com/profile/01955234977479398457noreply@blogger.comtag:blogger.com,1999:blog-393324845011978943.post-47410309665754106552009-06-04T13:03:47.958-04:002009-06-04T13:03:47.958-04:00Hi Eli,
With the clarification made to 'From ...Hi Eli,<br /><br />With the clarification made to 'From Classical to Quantum', there's a new guess in this writeup that stands out as requiring motivation (also tough). Namely, your <br /><br />"making the substitution $latex \vec{p} = i \hbar \nabla$"<br /><br />In Liboff, this is also pulled out of a magic hat. The only good motivation that I've seen for it was in Bohm's QT book, where it follows by Fourier transforms to switch from a position to momentum representation for the wave function. If anybody actually successfully studies from Liboff's text I imagine they also wonder where this comes from ... perhaps a topic for another blog;)Peeter Joothttps://www.blogger.com/profile/13747647271625793131noreply@blogger.com