Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates.
This book is an introduction to both the local and global analysis of eigenfunctions.
The emphasis is on the global methods and the use of Fourier integral operator methods to analyse norms and nodal sets of eigenfunctions.
American Mathematical Society Eigenfunctions of the laplacian on a riemannian manifold, paperback/steve zelditch
