Quantum physics i, lecture note 5 mit opencourseware. Remember that the pseudo norm s of a fourvector does not depend on the frame of reference in. It has no physical basis except that of the photon. This is the plane wave equation describing a photon. Einstein related the energy of particle matter to its mass. On the left side we have the wave property, wavelength, and on the right in a reciprocal relationship mediated by the ubiquitous planck s constant, we have the particle property, momentum. Finally, we require the wave equation to conform to bohr s correspondence. The above equation is derived from maxwell s equations which governs em waves in electrodynamics 9.
The fields of the matter waves satisfy maxwell s equations, the schrodinger. Electromagnetic radiation, exhibit dual nature of a particle having a momentum and wave expressed in frequency, wavelength. The wave length has to satisfy standing wave condition k 2. However, schr6dinger s equation itself, because of. Application of fermat s principle for this wave then is identical to the principle of least action applied to a material particle. The particle s energy, which is purely kinetic, k12mv2, is thus also quantized. About the channel in this channel, you will find easiest explaination of graduation post graduation physics topics. Introduction originally, schr6dinger regarded the wave intensity, gtqj, as the actual density of electric charge, and this gave an image of the electron as a unique and independent reality. Compton s formula established that an electromagnetic wave can behave like a particle of light when interacting with matter. Historical origins of quantum mechanics blackbody radiation, the photoelectric e. It was always a wave in its own right, or a superposition of such waves, as described in the thesis, and it is on the thesis that we now concentrate. It basically describes the wave nature of the electron. Using classical wave equation the 1d equation for an electromagnetic wave is expressed as 22 222 e1e 0 xct. Finally, we require the wave equation to conform to bohr s.
For photons, this relation is a straightforward consequence of e hf since a light wave has p ecand f c, where cis the speed of light. The wave particle duality seems to used all the time to explain quantum mechanics to the public, but it is one of my pet peeves. Indirectly this can be achieved by elevating the attributes that follow from vacuum superfluidity into fundamental guiding principles. By a formal derivation of the operator product remember. Physical significance of wave function the wave function has no physical meaning. Bohmian mechanics stanford encyclopedia of philosophy. In quantum mechanics, matter is believed to behave both like a particle and a wave at the submicroscopic level. But then, the wave nature of electromagnetic radiation is called into question when it is involved in blackbody radiation, photoelectric e ect and such. Quantum mechanics has paved the way for new engineering inventions and. How did schrodinger obtain the schrodinger equation. If, for example, the wave equation were of second order with respect to time as is the wave equation in electromagnetism. Since for a photon, e pc and e hf, the energy can be written as. The application of these ideas to the periodic motion of an electron in a bohr atom. The value of the wave function associated with a moving particle at point x,y,z and time t gives the probability of finding the particle at that time and at that point.
Finally, two additional meanings of the compton wavelength are derived. It was always a wave in its own right, or a superposition of such waves, as described in the thesis, and it. Deriving time dependent schrodinger equation from wave. Pdf derivation of the missing equations of special. Although he originally wanted a career as a humanist and even received his first degree in history, he later turned his attention to physics and mathematics. However, there is remarkably little g eometric or physical interpretation.
The eulerlagrange equations and hamilton s equations. The guiding equation can be derived in a similar fashion. The results established the first experimental proof of quantum mechanics. On the left side we have the wave property, wavelength, and on the right in a reciprocal relationship mediated by the ubiquitous planck s constant, we. Then, according to maxwell s wave equation, the differential equation of the wave motion in three dimensions is 2 2 2 1 2. But then, the wave nature of electromagnetic radiation is called into question when it is involved in blackbody radiation, photoelectric e. However, this equation contains an anomaly regarding the wave function propagation velocity. Also given a strict derivation of the heisenbergs uncertainty. Rays of this wave are identical to trajectories of a particle chapter 2. Schrodinger s equation can be derived by using einstein s light quanta hypothesis. Einstein had shown that a complete description of cavity radiation requires both the particle and wave aspects of cavity radiation. Let s substitute this equation into our wave equation and see what we find.
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