Can Quantum Mechanical Two-State Theory model Coulomb’s Force?
The quantum mechanical description of the four fundamental forces of nature is very important for the decryption of the rules which underlie our world. While Quantum Electrodynamics (QED) describes the electromagnetic force in great detail, it also uses complex mathematical techniques and advanced physical concepts. In the following, I will analyze to what extent a quantum mechanical two-state model can be used to describe the Coulomb interaction between two charged particles. To do so, I will exclusively focus on the electrostatic interaction, leaving dynamics aside. Furthermore, the analysis is nonrelativistic and does not consider the spin of the particles. Finally, using discrete state theory allows to explore the strength of the basic concepts of early quantum mechanics. In this sense, I will try to develop a simpli ed model for the quantum mechanical description of the electrostatic force. However, the analysis is not simplistic, since the traditional formalism of quantum mechanics will be used, including Dirac's Bra-ket notation, probability amplitudes, the Hamiltonian matrix as well as the Schrödinger equation. To understand the framework of my project, it may be helpful to take a look at the source of inspiration for my analysis: In Chapter 10 of the third volume of the well-known textbook series The Feynman Lectures on Physics[4], the force holding the hydrogen molecular ion together is explained in terms of a two-state system. The electron of the molecular ion can be either at the rst proton or at the second one. The exchange of the electron between both protons leads to an attractive force between them. It is known from QED that the electrostatic interaction between two charged particles is due to the exchange of a virtual photon which acts as force carrier. The idea of my work is to explore whether the electrostatic force can be described by a very similar model, replacing the electron acting as force carrier in the molecular ion by a virtual photon for the description of the electrostatic force between two charged particles. To describe a system consisting of charged particles, I will make the assumption that a charged particle can appear in two states. Either it is in state e where it can emit a photon or it is in state a which enables it to absorb a photon. Upon emission or absorption of a photon the charged particle transitions to the respective other state. This makes the approach analyzed in my work an element of discrete state theory, since two di erent states of the particle are used to store information about it. Of course such a model cannot be compared to the sophisticated theory of Quantum Electrodynamics. The point is, however, that it is interesting to explore the power of the most fundamental concepts of quantum mechanics and to show that such an analysis can lead to inspiring results.
果蠅(Drosophila melanogaster)的習得性無助表現之研究
習得性無助是個體經多次追求獎賞或逃離困境失敗後產生的一種消極行為表現。習得性無助的行為研究雖多,但對其神經機制的研究卻甚少。 本研究發現273,cha-Gal80>CsC-mCh是適合光遺傳學訓練的果蠅殖系。在白光點獎賞記憶訓練中,使273,cha-Gal80>CsC-mCh果蠅學會白光點視覺訊號代表著獎賞,並發現其白光獎賞記憶能持續7分鐘以上但未達10分鐘。藉已建立白光視覺訊號與獎賞連結的273,cha-Gal80>CsC-mCh,發現重複追求獎賞失敗的實驗組,相較於持續接受獎賞與完成獎賞記憶訓練而無任何操作的對照組,明顯表現習得性無助,本研究亦發現習得性無助個體也表現了活動力、覓食表現及攝食動機的下降。 本研究成功建立高成效的果蠅成蟲光遺傳學習得性無助訓練,並針對果蠅成蟲的習得性無助行為表現進行完整的研究,未來期望本於此訓練方式進行特定腦區、神經群和神經傳遞物之探究,建構果蠅習得性無助的神經網路機制。