The Development of Quantum Mechanics
(Niels Bohr)
Over the years, scientists and in particular, physicists have worked tirelessly in qualifying and understanding quantum theory. There have been heated arguments over theories and the like and these arguments continue to take place even today. Some of the contributors are mentioned in this outline.
Bohr's Explanation of the Periodic Table
In 1922, Niels Bohr developed an explanation of the atomic structure that underlies the regularities of the periodic table. He considered that atoms are built up of shells of orbiting electrons (part of his model of the atom, derived from Rutherford's work) with shells filled by, in the case of uranium, 2, 18, 32, 18 and 6 electrons. Uranium is the element with the highest naturally occuring atomic number. He couldn't, however, explain why these were the maximum numbers of electrons in the shells. No 72, Bohr predicted, when found would not have the properities of a rare earth element but have a valency of 4, something like zirconium. Scientists who worked on this found that Bohr was correct. In the same year (1922) Bohr was awarded the Nobel Prize.
Heisenberg and Bohr
Werner Heisenberg heard Bohr's lectures on the periodic table and although he was impressed, he wasn't convinced and thought he found some gaping holes in Bohr's theories. He objected to one of Bohr's statements. Bohr identified him as a "smart person" and admired his determination and courage to speak out against him. Bohr and Heisenberg went to Copenhagen to jointly work on quantum theory. Heisenberg rejected Bohr's electron orbits idea mechanically, but looked into it numerically.
Heisenberg Develops Quantum Mechanics
In May 1925 Heisenberg developed his mathematical theory of quantum mechanics. In the next few months he worked with Max Born and Pascual Jordon to develop what he called 'a coherent mathematical framework, one that promised to embrace all the multifarous aspects of atomic physics.'
(Bohr - Heisenberg - Pauli)Pauli Applies Quantum Mechanics to Hydrogen
Wolfgang Pauli, with much difficulity successfully applied it to the Hydrogen atom. He derived Balmer's equation as well as Rydberg's constant using quantum mechanics instead of numerical manipulation. Bohr did the same thing in 1913, but he did it with incosistencies between Classical Mechanics and Quantum Mechanics - he was very happy that his theories were supported by Quantum Mechanics alone.
Pauli's Exclusion Priniciple
From the Bohr model of the atom, the first quantum number specified was the principal quantum no , n, the second quantum number was the angular momentum number, l, and the third was the magnetic quantum number, m.
Pauli used these and came up with another quantum number. In 1925, Pauli's fourth quantum number - the spin number was introduced. This he felt could explain the maximum number of electrons in each shell. The maximum number of electrons coresponded to the number of different sets of quantum numbers available for each shell. Pauli's exclusion principle states that no two electrons can have the same set of quantum numbers.
The exclusion principle provided the reason for electrons in atoms being arranged in shells with the maximum number of electrons being 2, 8, 18, 32, 18, 8 from the first to the sixth shell.
Schrodinger Thinks Different:
Einstein's involvement ensured that De Broglie's work on the wave nature of particles was understood and appreciated by many, having read this work, Erwin Schrodinger in 1925 read a comment of Einstein's about the De Broglie theory. Schrodinger was certain that the comment which Einstein made was much more than just an analogy of De Broglie's work. Schrodinger set to work upon restoring concepts of waves to quantum theory. He derived equations that were similar to equations which explained real waves. It seemed that Schrodinger's work had brought Quantum closer theory to a much more palatable area - Classical Mechanics.
However, it was not long until scientists, including themselves, discovered that Heisenberg's and Schrodinger's approaches were very much the same thing - only different versions. Schrodinger was very dissapointed that his "waves" were not waves at all, they were just theoretical analysis given to the electron orbits. Max Born found a way to interpret Schrodinger's waves; he related them to the probability of finding an electron at a particular location.
Heisenberg's Uncertainty Principle:
Heisenberg after seeing Born's work set out to continue the idea of an electron's location further. In 1926, Heisenberg showed that uncertainty was an inherent property of all quantum mechanics. He showed that if the velocity of an electron is accurately found, then the position of it cannot be and vice versa. This of course led to his famous equation:
Although he did not realise at the time, this breakthrough has laid the foundations for all quantum mechanics.
(Fermi - Dirac - Heisenberg)
The Dirac Equation:
Paul Dirac extended quantum mechanics further. He derived the equation which added relativity to quantum mechanics. It correctly predicted the spin of electrons (which is a relativistic effect). Dirac also predicted the existence a particle like the electron with a positive charge. This was then named the positron when Anderson observed it in 1932. Dirac also explained that the equations of quantum and classical mechanics are not that dissimilar. He explained that classical mechanics' equations can be derived from quantum mechanics when using large quantum numbers or using Planck's constant as zero instead of h (6.626 E -34).
Now that I have completed my most exhaustive post ever, I'll leave you all with a quote that is entirely applicable to the above:
I think it is safe to say that no one understands quantum mechanics.
- Richard Feynman
This entry was posted by Blogpur, on
Wednesday, October 05, 2005.
You can leave your response.
6:56 PM
Venkat,
I find quatum mechanics concepts baffling but fascinating. Have you read the book,
Probabilities of the Quantum World by Daniel Danin ? . It gives a very good account of the history of Quantum Physics. Unfortunately my tryst with physics came to an abrupt end once I joined engineering profession.
9:53 PM
I haven't read it, but now that you have mentioned it, I'll go take a look in my library to see if I can find a copy! Thanks for your input. If it's not too much, what type of an engineer are you?
Quantum Mechanics can be very baffling, I don't think I have a very good understanding of it. What I understand, is what I've written!
10:51 PM
Venkat,
I gardauated as a Telecommunication Engineer .
The book , BTW is a translated one from Russian language.
Going by your writings, you do have a very good understanding of physics...
4:44 AM
hey venkat, nice write up. is/was physics your major?
7:37 AM
Thanks for the compliment Prabhu.
I haven't decided my major Sowmya - I am a Computer Engineer, I just read and understand this on my own accord! I find it interesting.
4:29 PM
Actually, that is slightly incorrect, I am about to do Computer Engineering...
8:00 AM
Karthikeyan,
While Max Planck was the father of the actual concepts of the idea of "quanta" I don't think he was involved in any great deal with quantum mechanics itself.
Aren't we all beginners when it comes to quantum mechanics!
Something about Indian railways is probably up next!
3:38 PM
Venkat.
I don't know how you can ignore Max Planck ?
Do drop in at Histroy of QM
Cheers
5:01 PM
Thanks for the site Karthik (if I may call you that)
I did not ignore Max Planck, i purposefully left him out. If I brought him in, then I would have to bring in Einstein and his explanation of the photoelectric effect and this was a different tangent to where I wanted to go --- thats why I left him out.
I understand that Max Planck was the father of all this - but I felt he was too far away from what I wanted to project.
5:46 PM
Go ahead. Have a ball and call me Karthik.
1:06 AM
hey do you want to host the next Scian Melt? I am hosting one on Oct 15th. The next one will be Nov 5th i think. Let me know and I'll add you to the schedule.
2:22 AM
Quantum Physics -- Check this link out!
I haven't seen/heard them, but will do so soon. Got the link from The Scientific Indian
enjoy!!
8:35 AM
Thanks Sowmya, I will check it out.
6:47 PM
Oh! Great!
I was under the impression that the desi blogosphere is largely devoid of Physics posts. This does motivate me to start doing physics posts on my blog. Thanks Venkat.
And as Venkat pointed out.. though Plank, Einstein were central to the 'quantum' ideas in 1900s, they weren't part of the work to give a rigid formulation of quantum mechanics. These facts may be of interest :
1. it was Max Born who first gave the "probabilistic" interpretation for the wave function.Heisenberg initiall y thought that the wave function relates directly to "matter density". The probablistic interpretation is probably the central tenet of quantum mechanics.
2. Dirac was the one who gave an elegant way of arriving at the rules of quantum mechanics.. through "state-vectors" etc etc. QM is best presented in Dirac's way. His "Principles of Quantum Mechanics" is a wonderful book and and has few equals.
7:47 PM
Thanks for your comments Aswin!
There are physics fanatics aswell! Your points are very interesting and pertinent to the topic. I will visit your blog.
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7:07 AM
Your blog keeps getting better and better! Your older articles are not as good as newer ones you have a lot more creativity and originality now keep it up!
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