## quantization

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

605357751
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### quantization

How does Schrodinger’s approach improve on Bohr’s explanation of quantization?

Andrew Pfeiffer 2E
Posts: 79
Joined: Sat Sep 28, 2019 12:16 am

### Re: quantization

From the Schrodinger equation (which isn't really applied directly in textbook calculations) one can calculate the wave function for any particle, as well as its corresponding energies. Now, the application of the Schrodinger equation to quantization comes from a thought experiment involving a particle in a box (i.e. a single particle of mass m confined in a one-dimensional box between two rigid walls a distance L apart). From the particle in a box, one can eventually find the equation

En = n2h2/8mL2 for n = 1,2,3

and because the equation can only take integer values for n, the energy of the particle is quantized (restricted to discrete values). This largely has to do with the idea of standing waves, brought up by the particle in a box. A guitar string can only support certain shapes which have zero displacement at each end, because they're tied down at either end. So in short, the Schrodinger equation (and its further applications) expand upon the abstract theories of quantization by providing a mathematical function true to wavelike properties of a particle.