PHYSICS 70 Chapter Notes - Chapter 40.1-40.3: Photon, Standing Wave, Matter Wave
3 Jan 2017
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If wave function known, can predict probabilities of detecting it in some given region. Schrodinger equation: particle with mass m and mechanical energy e, whose interactions with environment can be characterized by one dimensional potential energy function u(x): Particle characterized by wave function in quantum mechanics (cid:4666)(cid:4667) Identify lambda with de broglie wavelength of a particle, rewrite debroglie wavelength in terms. Goal is to find wave equation for which the solution would be wave function having debroglie wavelength. Success depended on ability to explain various phenomena refused to yield to classical- physics analysis and to make new predictions that were subsequently verified. Follows de broglie"s reasoning that matter is wave-like, where = /= /(cid:1865) Oscillatory wave-like function has the form (cid:4666)(cid:4667)=(cid:2868)(cid:1866)(cid:4666)2/(cid:4667) of particle kinetic energy (k): = /(cid:1865)= / 2(cid:1865) Debroglie wavelength increases as particle kinetic energy decreases. Solution to equation is the sinusoidal wave function where lambda is the debroglie wavelength for a particle with kinetic energy k.
