The formula the total energy of a covalent system is easily derived on such assumption that the overlap integrals between non-bonded orbitals are neglected.
This total energy of the system can be divided into three parts with the use of the mulliken's approximation of the moleclsr integrals. The first is the sum of the energies of the atomic valence states, the second is the sum of the interaction energies between the bonded atoms, and the third is the sum of the interaction energies between the non-bonded atoms. The first two parts give the bond energies. The last part gives the small contribution of the environment to the bond energies and may be neglected (This adds 0.32 eV. to the C-C bond energy in dismond.) We may prove the additivity rule of the binding energies of the saturated hydrocarbon and their related molecules on the above described assumptions.
Using the Slater's atomic wave functions, we have obtained 3.67 eV. as the value of the C-C bond energy, which is very closed to the observed one (3.713 eV. in diamond), although we have neglected the contribution from the exchange integrals between non-bonded orbitals.

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最近朝永教授によつてcollective motionを扱う一般論が展開された.固体論に於けるcollective motionの代表的のものの一つはスピン波の運動である.Heitler-Londonのmodelに立つspin waveの理論は比較的簡単であつてその扱う自由度はspinの自由度だけであるのに対して集合電子模型では電子のspin wave motionと軌道運動とが密接にからみ合つていて前者に比べて取扱いが複雑である.この小論の目的は集合電子模型に基いたspin waveの問題を朝永の方法によつて調べることである.一般の帯構造をもつ場合をsimplifyして自由電子模型によつてこの問題をとり扱う.集合電子模型によるスピン波の理論はHerring-Kittel. Herring2, 3, 4によつて議論された.特にHerringは自由電子模型で電子のスピンの平均の方向がZ軸に垂直に且つspiral状に変化している場合のエネルギーの値, 或は外部から強制的にM×R sin x なるtorqueが仂いた場のspinのresponseを求めexchange stiffnessconstantを計算した.そしてspin波のexcitationのエネルギーをこの常数から現象論的に求めた.これに対してこゝでは直接spin waveの性質を調べるわけである.方法はHerringのと全く異つているがexcitaion energyに関しては完全に同じexpression が得られる.

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このノートの目的は「電子と格子振動の相互作用と集団記述」と云うタイトルのもとで同誌2.3.4月号に発表した論文 [I]. [II]. [III] [これを [A] として引用する] に於て犯した計算上の誤診 [[A] の (3・11) のこと] とそれに由来する誤つた論述を訂正仕直し且統括して [IV] で述べる多電子束縛状態への考察の足掛りとすることである.

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The behaviors of perfect charged Bosons in the uniform magnetic field are treated.Their thermodynamic-and magnetic-properties are shown graphically, and we especially discuss the features of the susceptibility in the limit of vanishing field.

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A non-relativistic theory of displacement collisions by fast charged heavy particles passing through the mono- atomic stopping material has been presented in the previous paper.
It is shown that the theory can be applied to the poly-atomic stopping material in the non-relativistic case.
and to the relativistic case.

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