Eigenvalue bounds for polynomial central potentials inddimensions
نویسندگان
چکیده
منابع مشابه
Eigenvalue bounds for polynomial central potentials in d dimensions
If a single particle obeys non-relativistic QM in R and has the Hamiltonian H = −∆ + f(r), where f(r) = ∑k i=1 air qi , 2 ≤ qi < qi+1, ai ≥ 0, then the eigenvalues E = E (d) nl (λ) are given approximately by the semi-classical expression E = min r>0 { 1 r2 + ∑k i=1 ai(Pir) qi } . It is proved that this formula yields a lower bound if Pi = P (d) nl (q1), an upper bound if Pi = P (d) nl (qk) and ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2007
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/40/44/020