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I know the Schrodinger Equation is a key part of quantum mechanics. I am trying to understand it’s applications. Let’s say a team of engineers wants to build a laser from scratch, assuming they have the raw materials and tools at hand. At what point in the process would they need to use the Schrodinger Equation in order to complete the task.

Lambda
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  • The Schrodinger equation does not explain photons, stimulated emission, or lasers. But it does explain atoms and molecules quite well. – G. Smith Jun 07 '19 at 02:17
  • Would they need QM at all to build the laser? – Lambda Jun 07 '19 at 02:22
  • The Schrodinger equation determines (to a good approximation) the energy levels of atoms and molecules and thus the frequencies of laser light that they can emit. So I’d say yes. – G. Smith Jun 07 '19 at 02:30
  • The lasing process is explained by quantum physics in the form of quantum electrodynamics, which does describe photons and stimulated emission. There is more to QM than the Schrodinger equation. – G. Smith Jun 07 '19 at 02:33
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    @Lambda I'm a bit confused as to what you're asking. Quantum mechanics is required to understand the workings of a laser and therefore to design one, but you seem focused on building one, for which one would need little more than a sufficiently detailed list of instructions. – J. Murray Jun 07 '19 at 02:46
  • Just trying to get a hold on a real whole specific application. – Lambda Jun 07 '19 at 02:48
  • Applications of quantum theory are well documented and as a result I'm voting to close under the "homework-type question" rule for insufficient prior research. This is also a "list" type question which would also be generally discouraged as they generally have no definitive answer. One of the first uses of Schrodinger's equation is the evaluation of Hydrogen's theoretical spectrum - what else is required ? – StephenG - Help Ukraine Jun 07 '19 at 03:20
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    How are you defining "need"? A team of engineers could find plans to build a laser only needing some basic soldering skills and a supplier who can give them some optics and chips and stuff. – tpg2114 Jun 07 '19 at 03:20
  • Just close the question. I was just looking for one or two examples how it is applied. Apparently, you think that’s not reasonable. Close it. – Lambda Jun 07 '19 at 03:25
  • @J.Murray: The reference to engineers in the OP's questions implies that the laser still needs to be designed. If you had a list of instructions of how to build it, then you would not need engineers anymore. – flippiefanus Jun 07 '19 at 04:24
  • If you wanted examples of the application of the Schrodinger equation, ask for that. That would give people answering the freedom to construct scenarios where an engineer might need such an equation. In practice, engineers tend to avoid needing to do such calculations (we avoid them like the plague), because we have hundreds of other things to pay attention to when turning an idea into a product. To answer your question, we'd need the freedom to specify a product that actually calls for such extreme calculations. – Cort Ammon Jun 07 '19 at 05:30
  • I don't know of any examples myself, but my gut instinct is that the Schrodinger equation will show up in some sensing apparatus. The things we do to see further/sharper/dimmer are extraordinary. – Cort Ammon Jun 07 '19 at 05:33
  • This question is closely related : https://physics.stackexchange.com/questions/408539/is-a-purely-classical-description-of-lasers-possible – my2cts Jun 07 '19 at 05:59

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When engineers are given a task to design and build a system, it usually involves a set of specifications. In the case of a laser, the specifications would naturally include the wavelength of the required laser radiation, among other things. If we assume that the raw material does not already include the material for the active medium associated with that wavelength, then the engineers would have to do some calculations to determine what material they need that would produce light with that wavelength. This calculation would require some rudimentary quantum mechanics, because the wavelength is associated with the energy separation between two energy levels in the material.

There are also other specifications, such as the amount of power that the laser must produce. Perhaps, it would even include the power efficiency of the system. To design a system that satisfies these requirements, the engineers would have to use the laser rate equations, which comes from Einstein's analysis of stimulated emission. These equations also involve basics from quantum mechanics.

So, although the Schroedinger equation may not be used directly in the design process, other aspects of quantum mechanics play a role in the design process.

flippiefanus
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  • Thanks for the answer. I was always under the impression that QM was essential to laser development. – Lambda Jun 07 '19 at 13:56