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Wavefunctions and states 
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#1
Mar712, 10:34 PM

P: 887

this reminds me of a question that I'd like to ask.
as a chemist, my view of quantum mechanics is that it is a useful tool to give the right answer for spectroscopy calculations and to make a model of complicated molecules so that we can pin down some parameters with instruments, then get the whole molecule's structure. however, i keep reading on some book reviews at Amazon that the "core of quantum mechanics is not the wavefunction, but the state". What is that supposed to mean? I never paid attention to the "philosophical" meanings of quantum mechanics. All that mattered was knowing how to calculate the wavefunction for various boundary conditions and knowing how to use them. that was until I took a look at the first few pages of Desai's book and didn't actually see many wavefunction symbols in there. this is important news to me because i'm entering a MS in physics soon and don't want to slam into a brick wall due to "learning QM wrong". 


#2
Mar712, 10:54 PM

P: 1,042




#3
Mar712, 11:30 PM

P: 887

i still can't understand the Wiki page. 


#4
Mar712, 11:40 PM

P: 1,042

Wavefunctions and states



#5
Mar812, 02:16 AM

P: 660

Wave functions are just one way to represent a quantum mechanical state.
In many cases you can derive the physics of a simple system by just knowing the Eigenvalues of an operator (or a few operators, for example angular momentum or spin), you don't have to determine the complete wave function. The states then can be written in vector form, and the operators as matrices. (that is why expectatoin values are often called matrix elements) We can then do all the fun physics using simple matrices and leave the derivation of the exact wave functions to the chemists :) The BraKet notation is particularly useful for that. 


#6
Mar812, 02:29 AM

P: 887

i think i will have to cut my vacation this summer short and spend a month at academic boot camp relearning quantum. 


#7
Mar812, 02:48 AM

P: 1,042




#8
Mar812, 06:40 AM

P: 1,412

My intention is not to go offtopic or something, but I'm just wondering if you realize that the naive approach you're painting (or am I misinterpreting?) doesn't seem to create a coherent picture. Just trying to get you to think about it :) not trying to belittle/act superior... 


#9
Mar812, 07:14 AM

P: 419

To OP: In the common understanding in quantum chemistry and all parts of solid state physics I am aware of, a 'state' and a 'wave function' are the different names for the exactly same thing (and for oneparticle wave functions, a further synonym is 'orbital', but unlike orbitals, states and wave functions also come in Nbody varieties). Maybe some physicists like to emphasize different aspects of wave functions with the two words, but there is little reason to go with them. You have not learned quantum mechanics "wrong".
EDIT: Okay, maybe one note: In statistical mechanics, some there also are "nonpure states", described by thermodynamic (ensemble) density matrices (projectors onto wave functions). Those density matrices represent ensembles of wave functions (not single wave functions) and can and often are regarded as "states" themselves, as they are the maximal description of statistical ensembles. However, in some sense they are not as fundamental as wave functions, because statistical quantum mechanics can be derived from standard quantum mechanics alone and a few statistical assumptions (ergodicity principle etc). Maybe the author was referring to that. But unless you are working with statistical mechanics, there is not need to regard such density matrices as fundamental 'states'. 


#10
Mar812, 09:00 AM

P: 66




#11
Mar812, 01:20 PM

P: 419

Thus, there is no reason to regard density matrices as the fundamental objects instead of wave functions, because both formalisms can be derived from each other. And I personally find it hard to regard density matrices as anything but calculation tools to use when lacking some information about about a system, but this is only a matter of taste, nothing more (in both ways!). 


#12
Mar812, 09:54 PM

P: 887




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