Posted by Steve Simon on April 18, 2014, 9:05 am, in reply to "Decaying waves in 1D chains"
I'm glad you are trying some of these extra problems! Yes, you are supposed to get a complex k (and solutions should come in complex conjugate pairs). If you write k = Real + i Imag or k=Real  I imag, then the waveform is e^{i w t  i k n a} as usual, but k is complex. Rewrite this exponential as e^{i somethingreal} e^{+n a Imag} or e^{i something real} e^{n a Imag} which shows this particular wave has a decaying envelope with the decay length set by the imaginary part of k. 
12 
Message Thread
