Can Dumbbell-Shaped Orbitals Be Experimentally Confirmed?

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If you solve the Schrodinger Equation, you will get solution for the equation, which is orbital.

My question is, for example, dumbbell-shaped p-orbitals in hydrogen atoms or other atoms,
is there some expert who visualized this orbitals and confirmed experimentally?

And how can it be confirmed experimentally, that p-orbitals exist in a shape of dumbbell?
 
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Orbitals are a particular choice of single electron basis sets, which can be used to make the basis sets for many electrons. The wave function for N electrons is in 3N-dimensional configuration space, so it doesn't have an easy visualization. The wave function for a single electron is in a 3-dimensional configuration space, so it can be visualized as being in space.

http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/basis-sets.pdf
 
What does it mean to exist? We can assemble pictures out of statistics of measured data. Does that count?
http://io9.com/the-first-image-ever-of-a-hydrogen-atoms-orbital-struc-509684901
The simple answer is no, they don't exist. They are just idealized models. Does the frictionless mass m (which is so frequently present in undergraduate physics) exist?
 
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Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
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The lesser Green's function is defined as: $$G^{<}(t,t')=i\langle C_{\nu}^{\dagger}(t')C_{\nu}(t)\rangle=i\bra{n}C_{\nu}^{\dagger}(t')C_{\nu}(t)\ket{n}$$ where ##\ket{n}## is the many particle ground state. $$G^{<}(t,t')=i\bra{n}e^{iHt'}C_{\nu}^{\dagger}(0)e^{-iHt'}e^{iHt}C_{\nu}(0)e^{-iHt}\ket{n}$$ First consider the case t <t' Define, $$\ket{\alpha}=e^{-iH(t'-t)}C_{\nu}(0)e^{-iHt}\ket{n}$$ $$\ket{\beta}=C_{\nu}(0)e^{-iHt'}\ket{n}$$ $$G^{<}(t,t')=i\bra{\beta}\ket{\alpha}$$ ##\ket{\alpha}##...
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