Over 10 million scientific documents at your fingertips. He further reasoned that matter would obey the same. It seemed reasonable to wonder if electrons could also have a dual wave particle nature. We will be concerned with wave mechanics here, the oldest form of quantum mechanics. Chapter 41 wave mechanics department of physics, nthu. It features a 1hour lecture video, and also presents the prerequisites, learning objectives, reading assignment, lecture slides, homework with solutions, and resources for further study. This page contains materials for the session on particle wave duality. The wave properties of particles mean that when you confine it in a small space its momentum and kinetic energy must increase. Waves possesses particle type character inherently, not. This worksheet comes complete with a full answer sheet and extension questions to keep those advanced boffins busy. Because the schrodinger and other wave equations for massive particles were conceived as. With the addition of two new quantum numbers, the bohrsommerfeld theory accounted for many features of spectra and showed how the periodic table is built up in a systematic way. Enter the weird and wonderful world of wave particle duality.
Electron microscope is a common instrument illustrating this fact. Reinterpretation of matterwave interference experiments based on. A suitable geometric generalization of the wave equation 1. Compare the bohr and quantum mechanical models of the atom.
Matter waves istituto nazionale di fisica nucleare. A causal interpretation, elsevier publishing company, 1960. Sommerfeld refined bohrs theory by incorporating special relativity and the possibility of elliptical orbits. The probability shown as the color opacity of finding the particle at a given point x is spread out like a waveform, with no definite position of the particle. One way to do so is by interpreting the kg equation as describing a particle moving both forward and backward in time. Before taking up the question of the speed of matter waves, we prefer. Before i derive the equation, it is important to understand the debroglie hypothesis which i am sure. We know that light can be a wave as well as a particle. Einstein had shown that a complete description of cavity radiation requires both the particle and wave aspects of cavity radiation. In particular, we examine questions about existence and. Since the correct calculation is a bit complicated, we postpone it to section 5. It has a place in science history, but one shouldt take it too seriously because it detracts too much from what we know for good about the microscopic world.
The wave model of the electron can be used to explain the bohr model. It seemed reasonable to wonder if electrons could also have a dual waveparticle nature. In case my question is wrong, then please help me correct my thinking. In fact, to add some more weight to their narrative, theyll usually write them in a. The wave equation governs a wide range of phenomena, including gravitational waves, light waves, sound waves, and even the oscillations of strings in string theory. It expresses the inability of the classical concepts particle or wave to fully describe the behaviour of quantumscale objects. Matter waves are a central part of the theory of quantum mechanics, being an example of. Quantum physics i, lecture note 4 mit opencourseware. As albert einstein wrote it seems as though we must use sometimes the one theory and sometimes the other.
It basically describes the wave nature of the electron. But then, the wave nature of electromagnetic radiation is called into question when it is involved in blackbody radiation, photoelectric e ect and such. Schrodingers, diracs and proposed equations with the universal wave equation is also presented. The mathematics of pdes and the wave equation michael p. University of calgary seismic imaging summer school august 711, 2006, calgary abstract abstract.
The wave equation 2 for the momentum p follows automatically from the theory of special relativity which will be shown. This equation simply relates the wave character and the particle character of an object. Gupta, in principles and applications of quantum chemistry, 2016. The debroglie equations can be derived from the einsteins famous equation of energymass equivalence and planks theory of quantum radiation. The momentum p is found to dependent on the phase change rate over space resulting in the debrogle matter wavelength p h. In that case, we can say that equation 1 and 2 represent the same quantity. Aug 31, 2016 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.
If waves, such as electromagnetic radiation, can sometimes act like particles as seen with photons, then why couldnt particles, such as electrons, sometimes act. The matterwave theory was gracefully incorporated by heisenbergs uncertainty principle. Since light can behave both as a wave it can be diffracted and it has a wavelength and as a particle it contains packets of energy h. Our new crystalgraphics chart and diagram slides for powerpoint is a collection of over impressively designed datadriven chart and editable diagram s guaranteed to impress any audience. Waveparticle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. The examples of both particle nature of light and wave nature of light are provided here at byjus. Thus, every object in motion has a wavelike character. What links here related changes upload file special pages permanent link page. However, as we will show later, this is not the speed of the particle. It is represented by the wavelength of a wave traveling at constant speed is given by.
Time independent schrodinger wave equation duration. Shortly after it was published in t he fall of 1925 pieter debye, a. Quantum mechanics is a theory of information it is a set of laws about the information that can be gained about the physical world. The waveparticle duality seems to used all the time to explain quantum mechanics to the public, but it is one of my pet peeves. Youll find them in almost any popular account of quantum mechanics, and the writers of those popular books will tell you that f is the frequency of the matterwave, and. The davissongermer experiment proved beyond doubt the wave nature of matter by diffracting electrons through a crystal. Other examples of mechanical waves are seismic waves, gravity waves, vortices, and. Since v equation is a secondorder linear hyperbolic pde that describesthe propagation of a variety of waves, such as sound or water waves. This work is licensed under a creative commons attributionnoncommercialsharealike 4. By rearranging the momentum equation stated in the above section, we find a relationship between the wavelength. Chart and diagram slides for powerpoint beautifully designed chart and diagram s for powerpoint with visually stunning graphics and animation effects. To this end, the wave equation for a spinless free particle is proposed and it is argued from some specific examples that the linearity or nonlinearity of the wave equation seems to. Depending on the medium and type of wave, the velocity v v v can mean many different things, e.
Debroglie waves explain about the nature of the wave related to the particle. It represents an outmoded way of thinking old quantum theory. It means when the matter is moving it shows the wave properties like interference, diffraction etc. Electromagnetic radiation, exhibit dual nature of a particle having a momentum and wave expressed in frequency, wavelength. In physics, mathematics, and related fields, a wave is a disturbance change from equilibrium. When the elasticity k is constant, this reduces to usual two term wave equation u tt c2u xx where the. Plancks investigation of the emission spectra of hot objects and the subsequent studies into the photoelectric effect had proven that light was capable of behaving both as a wave and as a particle. Explains why its impossible to notice the wavelength of a fast moving car.
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