Xuefeng Liu

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math.NA2026

Guaranteed Lower Eigenvalue Bounds for Spectral Galerkin Methods with Application to SchrÃ¶dinger Operators

Xuefeng Liu

Spectral Galerkin methods are renowned for high-precision eigenvalue approximation, yet a rigorous lower bound obtained directly from a spectral discretisation has remained unavail…

math.NA2026

Explicit Two-Sided Eigenvalue Bounds for SchrÃ¶dinger Operators with Singular Potentials via Finite Element Method

Xuefeng Liu

We present, to the best of our knowledge, the first numerical algorithm for explicit, computable two-sided eigenvalue bounds for SchrÃ¶dinger operators H = -Delta + V on R^N, N = 2…

math.NA2026

Rigorous Eigenvalue Bounds for SchrÃ¶dinger Operators with Confining Potentials on $R^{2}$

Xuefeng Liu

We propose a rigorous method for computing two-sided eigenvalue bounds of the SchrÃ¶dinger operator $H = - I^ + V$ with a confining potential on $R^{2}$ . The method combines doma…

Guaranteed Lower Eigenvalue Bounds for Spectral Galerkin Methods with Application to SchrÃ¶dinger Operators

Explicit Two-Sided Eigenvalue Bounds for SchrÃ¶dinger Operators with Singular Potentials via Finite Element Method

Rigorous Eigenvalue Bounds for SchrÃ¶dinger Operators with Confining Potentials on R2

Rigorous Eigenvalue Bounds for SchrÃ¶dinger Operators with Confining Potentials on $R^{2}$