Hi all, just joined the forums today, essentially to ask this one question which has been bugging me since I first started learning QM almost 2 years ago.(adsbygoogle = window.adsbygoogle || []).push({});

I'm basically trying to find solutions to the 1-D TISE for a square well potential.

My question is :- without making references to classical mechanics is it actually possible to predict anything using Quantum Mechanics and the schroedinger equation? Every book I've ever seen try to answer this problem has started with the line "We search solutions to the TISE in the form of standing waves". Is there anything to justify this action? Other than in the classical limit, this is how it works? This argument seems on thin ice...

I've heard people say that the Schroedinger equation is just like Newton's laws, but for quantum physics. Newton's laws don't ask me to search in the dark for solutions toF=ma. They ask me whatFis and then tell mea. The schroedinger equation asks me what [tex]\hat{H}[/tex] is and then I have to prod blindly in the dark for my eigenfunctions... Or have I misunderstood?

Or is it more that once I know the wave function, the TDSE will tell me how it advances through time. i.e. is knowing the wavefunction in QM just like knowing the mass in Newton's mechanics and the TDSE is just like Newton's laws?

If so, is there any other way of working out the wavefunction than this crazy "let's guess that it's like this" mathematics? (I guess measurement is the only way, but then, we get collapse of the wavefunction sometimes... and can never measure everything that's contained in the wavefunction as a result)

Please help me, this is bugging me immensely. Without this understanding, I don't think I can take QM seriously.

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# Solutions of TISE - is it all about groping in the dark?

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