By Masayuki Nagasaki, Mituo Taketani

ISBN-10: 9810246013

ISBN-13: 9789810246013

This e-book analyzes the difficult logical procedure wherein the quantum conception used to be constructed, and exhibits that the quantum mechanics hence validated is ruled via stereo-structural good judgment. the strategy of research is predicated on Mituo Taketani's three-stage thought of medical cognition, which used to be awarded and constructed in shut reference to Yukawa's thought of the meson. in accordance with the three-stage thought, medical cognition proceeds via a chain of coiling turns of the phenomenological, substantialistic and essentialistic levels. The previous quantum mechanics is proven to be in a substantialistic level, through the quantum mechanics within the corresponding essentialistic level.

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**Additional resources for Formation and Logic of Quantum Mechanics: Formation of Atomic Models**

**Example text**

45) Putting all Un's in this equation to be nU, he gets f(nU) = ±f(U). (46) The solution of this functional equation is f(U) = ^ . (47) Inserting this into Eq. (41), he has with a constant b > 0 d2S 1 (48) dW^'W b depends only on the frequency v. The integration of Eq. (48) gives — = const. -l- log U, (49) Atomistic Investigations of Black Body 21 Radiation from which Planck obtains with the use of the second law of thermodynamics dS/dU = l/T U = ae-blT , (50) a being a coefficient. Wien's displacement law shows that a = Au, b = Bu, (51) where A and B are numerical constants.

30 Atomistic Investigations of Black Body Radiation 31 or T =^ ) - (76) With the use of this expression of T the integration of the second law of thermodynamics dS = dU/T results in iii) S = G{^). The entropy of any resonator in the field of black body radiation is, therefore, depends on the single variable U/v. This is the simplest expression of Wien's displacement law. The application of Wien's displacement law to the entropy S given in Eq. (72) shows necessarily that the energy element e is proportional to the frequency v, so that e = hv.

Now, Planck discusses as follows. "One could for the moment tend towards the supposition that Sn depends on Un in the same way as S does on U. In that case, it would be possible to get the value of Sn by putting Un instead of U in the expression of S taken as a function of U. However, this supposition could not be founded by any consideration of a physical kind, since no physical meaning must actually at all be attached to the quantity of entropy, just as it is the case with the absolute quantity of a potential of force, for example.

### Formation and Logic of Quantum Mechanics: Formation of Atomic Models by Masayuki Nagasaki, Mituo Taketani

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