We know that all states of the wavefunctions must be quantized. Therefore, when we have a particle, say an electron, trapped in a well with infinite potentials on either side - let's set the boundaries to the traditional -1/2L to 1/2L - the ground state of the energy must give us a wavelength which must be, at most, 1/2lambda=L. We then can have n number of 1/2lambdas within the well, and we can describe those states alternatingly with Cos and Sin functions - but n must be a whole integer - otherwise the state is not quantized. Now, suppose we inject a single electron, at a velocity of .01c, let's be more specific about it and say 1x10^6 m/s, into a well that is 4 Angstroms wide - i.e. from -1/2L to 1/2L, we have a space spanning 4 Angstroms. We know, from the DeBroglie relation that the wavelength of the electron at that speed is approximately 7 Angstroms. What happens when the electron enters that well? Will the energy state immediately adapt to a quantized level - and if so, will it immediately fall to ground state or will it adapt to the nearest frequency which allows whole numbers of half wavelengths in the 4 Angstrom well? Or does the whole system just break down?(adsbygoogle = window.adsbygoogle || []).push({});

Jason

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# Question regarding 1-D PIW thought problem

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