= Parity-constrained variational bound
An even one-dimensional confining potential preserves even and odd <parity>. Restricting a normalized trial state to the odd sector makes its <Rayleigh quotient> an upper bound on the lowest odd <energy>, which is the first excited <energy> for the usual nonsingular one-dimensional bound-state problem. This avoids contamination by the even <ground state>. For an adjustable-width odd Gaussian, optimize its own width rather than borrowing the ground-state optimum.
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