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8 The Variational Principle - School of Physics and Astronomy
In practice, this is how most quantum mechanics problems are solved. ... the binding energy of a deuteron due to the strong nuclear force, with A=32MeV and a=2.2fm. The strong nuclear force does not exactly have the form V(r) ... chemistry, materials, minerals and beyond.
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www2.ph.ed.ac.ukThe spherical harmonics satisfy an orthogonality relation: * 2π 0 dφ * π 0 dθ sinθ, Ym1 l1 (θ,φ)-∗ Ym2 l2 (θ,φ)=δ l1,l2 δ m1,m2. Note that they are orthonormal, not just orthogonal, as the constant multiplying the product of Kronecker deltas is unity. 6.3.1 Completeness and the …
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www2.ph.ed.ac.ukexplicit form of the hydrogenic wavefunction from Lecture 10 u 100(r)= 1 √ π (Z/a 0)3/2 exp(−Zr/a 0) thus yields the expression ∆E 1 = e2 4π 0 Z3 πa3 0 2 1 r 12 exp{−2Z(r 1 +r 2)/a 0} dτ 1dτ 2 Amazingly, this integral can be evaluated analytically. See, for example, Bransden and Joachain, Introduction to Quantum ...
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www2.ph.ed.ac.uk(10) is an important result and is used frequently in electromagnetism, uid mechanics, and other ‘ eld theories’. Finally, when a scalar eld ˚depends only on the magnitude of the position vector r= jrj, we have r2 ˚(r) = ˚00(r) + 2˚0(r) r where the prime denotes di erentiation with respect to r. Proof of this relation is left to the ...
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