# Relationship between Schrodinger equation and string/membrane

In Sakurai's Modern Quantum Mechanics (2nd ed) p.99, he says

We know from the theory of partial differential equations that (time-independent Schrodinger equation) subject to boundary condition ($\psi(\mathbf{x}')\rightarrow 0$ as $|\mathbf{x}'|\rightarrow\infty$) allows nontrivial solutions only for a discrete set of values of $E$. It is in this sense that the time-independent Schrodinger equation yields the quantization of energy levels. Once the partial differential equation (time-independent Schrodinger equation) is written, the problem of finding the energy levels of microscopic physical systems is as straightforward as that of finding the characteristic frequencies of vibrating strings or membranes.

Although I've found a paper (http://www.scientificexploration.org/journal/jse_21_1_hocking.pdf) about this, the relationship is still not very explicit. So would you please explain briefly about the relationship between the Schrodinger equation and string/membranes? Many thanks.

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This question (v2) seems partly spurred by a conflation of non-relativistic material strings, such as, e.g., a guitar string, and relativistic string theory. –  Qmechanic Aug 5 '14 at 12:16