unit8_qm_sup - PHYS 302 Unit 8 Quantum Mechanics Supplement...

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PHYS 302 : Unit 8 Quantum Mechanics Supplement – Athabasca University 1 Unit 8 Waves: Quantum Mechanical Waves After completing this Unit 8 supplement, you should be able to 1. identify that particles have a wavelength, and define the de Broglie wavelength. 2. identify that wave effects similar to those explored in this course also apply to particles on some scale. 3. identify that free particles can have any energy, momentum, and wavelength. Introduction Historically, light had been regarded as a particle stream, a view established in the late 1600s by Newton and dramatically challenged by Young’s experiments in the early 1800s. Young’s experiments demonstrated that light obeys the principle of superposition. If light is made up of particles, it is easy to imagine more particles resulting in more light. However, with waves, the crest of one wave can line up with the trough of another, so that two light beams can combine, under the right circumstances, to give no light. This phenomenon, known as destructive interference , will be discussed quantitatively near the end of the course. Since Young observed destructive interference of light—hard to imagine in a particle-based theory of light, though destructive interference is an intrinsic property of waves—the prevailing view in the 1800s was that light was, in fact, a wave. This view received further credence when Maxwell, in the late1800s, showed that electricity and magnetism are not separate forces and that their union (electromagnetism) completely explained the (then) known properties of light and other forms of electromagnetic radiation. Quantization of Energy in Electromagnetic Radiation By the early twentieth century, the details of Maxwell’s theory had begun to fray. A complex argument allowed Planck to explain emission of radiation only if it was quantized (i.e., came in small bursts). Atomic theory, based largely on chemical experiments, had led to the realization that matter came in small chunks, now known as atoms. By the late 1800s, experiments with “vacuum” tubes had led to the conclusion that electricity flowed in thin gasses through the action of “corpuscular rays” that travelled in straight lines. In 1906, J. J. Thomson received the Nobel Prize in Physics for his 1897 conclusion that corpuscular rays were made up of small, negatively-charged particles that we now call electrons. The emission of electrons from the surfaces of certain materials when illuminated—the photoelectric effect—implied a link between the particulate properties of electrons and that of light. Photoelectric emission causes an electric current to flow out of a surface. As expected, such a current increased with an increasing level of illumination, but light shorter than a certain wavelength (the particular wavelength varied with the material) was required to cause any emission of electrons, no matter how bright the illumination. This was unexpected. This evidence strongly suggested that one particle of light ejected one electron, but only if that particle of light had enough energy to bump the electron out of the surface. This realization—not the special theory of relativity—also
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