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## Main Question or Discussion Point

for a Hamiltonian [tex] H=H_0 + \epsilon V(x) [/tex]

my question is (for small epsilon) can WKB and perturbative approach give very different solutions ?? to energies eigenvalues and so on the index '0' means that is the Hamiltonian of a free particle.

problem arises perhaps in calculation of:

[tex] \int \mathcal D [x] exp(iS[x]/\hbar)[/tex]

with the action [tex] S[x]=S_0 [x] +\epsilon V[x] [/tex]

here the main problem is that in perturbation theory the functional integral may be divergent (due to IR and UV divergences) but in WKB (semiclassical approach) the integral can be 'calculated' (given finite meaning),

hence i'd like to know if at least for perturbative case you can use WKB approach (with some re-scaled constant) to deal with perturbation theory..note that for the 'free particle' no interaction WKB gives exact methods..thankx.

my question is (for small epsilon) can WKB and perturbative approach give very different solutions ?? to energies eigenvalues and so on the index '0' means that is the Hamiltonian of a free particle.

problem arises perhaps in calculation of:

[tex] \int \mathcal D [x] exp(iS[x]/\hbar)[/tex]

with the action [tex] S[x]=S_0 [x] +\epsilon V[x] [/tex]

here the main problem is that in perturbation theory the functional integral may be divergent (due to IR and UV divergences) but in WKB (semiclassical approach) the integral can be 'calculated' (given finite meaning),

hence i'd like to know if at least for perturbative case you can use WKB approach (with some re-scaled constant) to deal with perturbation theory..note that for the 'free particle' no interaction WKB gives exact methods..thankx.