= Neumann-Dirichlet open-string boundary condition
{c}
{title2=$\partial_\sigma X(0)=0,\quad X(\pi)=y$}
= ND boundary condition
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{synonym}
A transverse <open string> coordinate has an ND boundary condition when one endpoint obeys a <Neumann boundary condition> and the other a <Dirichlet boundary condition>. On a strip of width $\pi$, its nonconstant spatial <eigenfunctions> are $\cos((n+1/2)\sigma)$ when the free endpoint is at zero. They solve the endpoint equations because their derivatives vanish at zero and their values vanish at $\pi$. Reversing the endpoints gives sine <eigenfunctions> with the same frequencies. The fixed endpoint removes the dynamical <worldsheet zero mode>.
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