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Experimental tests of BCS theory compare several properties of the same superconducting state. In the conventional weak-coupling setting, phonon-mediated attraction pairs opposite momenta and spins, and the BCS quasiparticle spectrum is $E_k=\sqrt{{\xi }_k^2+{\Delta }^2(T)}$. Agreement with a single energy scale and its temperature dependence is more discriminating than observing zero resistance alone.

The superconducting isotope effect tests the lattice's role. Replacing one isotope by another changes ionic masses while leaving the chemical valence nearly unchanged. Phonon frequencies scale approximately as $M^{-1/2}$, so a weak-coupling phonon mechanism predicts $T_c\propto M^{-\alpha }$ with $\alpha \simeq 1/2$ when other parameters stay fixed. The shift was measured in mercury before the microscopic pairing theory was developed.^[ref] Deviations from $1/2$ can result from Coulomb, anharmonic and strong-coupling effects; the isotope observation supports lattice-mediated pairing without uniquely proving every assumption of the simplest model.

Thermodynamic measurements test the gapped excitations and condensation energy. An isotropic fully gapped superconductor has exponentially small low-temperature electronic heat capacity, rather than the normal linear law. At the transition the weak-coupling BCS thermodynamic ratios areHere $C_n$ means the electronic contribution after subtracting the lattice background. The gap closes at $T_c$, and the same framework predicts the temperature dependence of penetration depth and thermodynamic critical field. These quantities were quantitative comparisons in the original theory.^[ref]

Electron tunnelling measures the excitation spectrum more directly. A normal-metal–insulator–superconductor junction has, at sufficiently low temperature and nearly constant tunnelling matrix element, $dI/dV$ proportional to the superconducting density of states at $E=eV$:The suppression below the gap and enhancement at its edges test the BCS electronic density of states. Giaever's thin oxide-barrier junction measurements established such energy-gap structure.^[ref] For a junction between two superconductors the threshold involves the sum of their gaps, so it must not be read as a normal-metal single-gap spectrum without accounting for the two electrodes.

Nuclear spin-lattice relaxation supplies a phase-coherence-sensitive test. In the conventional s-wave case, the Hebel-Slichter coherence peak just below $T_c$ is followed by a falling rate at lower temperature. Density of states alone is not enough: the BCS coherence factors enter the transition matrix elements. The contrast between nuclear relaxation and ultrasonic attenuation was explained using the paired state, unlike a simple two-fluid population model.^[ref]

Finally, magnetic flux quantization in units $h/(2e)$ and Josephson effects support a coherent charge-$2e$ condensate. Those observations establish pairing and phase coherence more broadly; their existence alone does not specify a phonon mechanism or an isotropic weak-coupling gap. The converging isotope, spectroscopic, thermodynamic and coherence-factor tests support conventional BCS superconductivity, with explicit limits to its simplest universal ratios.

Put $\xi =ϵ-{ϵ}_F$ and $\Delta =|\Delta |>0$. The BCS quasiparticle spectrum has $E=\sqrt{{\xi }^2+{\Delta }^2}$, so on either inverse branchConservation of states on one branch gives $D_{\mathrm{branch}}(E)dE=g({ϵ}_F)|d\xi |$. Consequently the single-branch expression requested in the source isThere are no such states for $0<E<\Delta$ in this ideal fully gapped model. Near the edge the density of states diverges as $(E-\Delta {)}^{-1/2}$, an integrable singularity; at large $E/\Delta$ it approaches its normal-state value.

Counting qualification. The energy map in the source is two-to-one. If $g(ϵ)$ literally counts all normal-state levels both above and below ${ϵ}_F$, the unweighted positive-energy quasiparticle density from a folded spectrum must sum both preimages, and is insteadAlready at $\Delta =0$, folding $\xi$ into $|\xi |$ doubles the positive-axis density. Thus the printed formula is not the unweighted count of all states under the literal mapping without an additional normalization convention.

There is also a standard physical quantity with exactly the printed normalization: the BCS electronic density of states, measured for example by single-electron superconducting tunneling. At positive $E$, the electron spectral weights of the two roots are the BCS coherence factors $u_{\pm }^2=(1+{\xi }_{\pm }/E)/2$. They sum to one, so the weighted sum is $g({ϵ}_F)E/\sqrt{E^2-{\Delta }^2}$. This supplies a valid electronic-DOS interpretation, while keeping it distinct from counting every positive-energy excitation. Spin degeneracy must be included consistently in $g$ and the transformed density; it does not remove the branch-counting issue.

A many-to-one change of energy variable requires summing every inverse branch. For $E(\xi )=\sqrt{{\xi }^2+{\Delta }^2}$ and constant normal density of states $g_F$ on both sides of zero, there are two roots for $E>\Delta$, giving $D_{+}(E)=2g_{F}E/\sqrt{E^2-{\Delta }^2}$. A single branch instead gives $g_{F}E/\sqrt{E^2-{\Delta }^2}$. The distinction persists when $\Delta \to 0$: folding $\xi$ into $|\xi |$ doubles a two-sided constant density on the positive axis. Spin degeneracy is a separate normalization choice; it must be applied consistently to both normal and transformed densities. The BCS electronic density of states has the single-factor expression because it is spectrally weighted rather than an unweighted branch count.