In this Letter we present new tunneling data on YBa2Cu3O7 thin films by low temperature scanning tunneling spectroscopy. Unusual peak-dip-hump features, previously reported in Bi2Sr2CaCu2O 8+δ , are also found in YBa2Cu3O7. To analyse these common signatures we propose a new heuristic model in which, in addition to the d-wave symmetry, the gap function is energy dependent. A simple expression for the quasiparticle density of states is derived, giving an excellent agreement with the experiment. The dynamics of the quasiparticle states and the energy scales involved in the superconducting transition are discussed.Getting to the heart of the quasiparticle density of states (DOS) in cuprate superconductors is an active goal of current theoretical and experimental research. Indeed, in the case of conventional materials, the quasiparticle DOS in the superconducting state contains the key information on the pairing. For this reason various methods, such as angle-resolved photoemission (ARPES), tunneling (TS) and Raman spectroscopies, as well as optical conductivity, are extensively used to elucidate the pairing mechanism in cuprates. Among these, scanning tunneling spectroscopy (STS), with its high spatial and energy resolution, emerges as the technique of choice.Using such a local probe at low temperature, reproducible vacuum tunneling spectra have been obtained on many cuprates [1][2][3][4][5][6][7][8], in particular Bi 2 Sr 2 CaCu 2 O 8+δ (BSCCO) and YBa 2 Cu 3 O 7 (YBCO). However, one still cannot interpret the experimental curves precisely. The shape of the DOS in BSCCO has a non-trivial dependence on doping [7,9,10], temperature [7,[9][10][11][12][13][14][15][16] and magnetic field [17,18]. The state density is characterized by its large value at the Fermi level, unusual quasiparticle peaks and dip-hump structures at higher energies (see Fig.1). While the T c vs doping curve is bell-shaped, the gap width decreases linearly, as the doping increases from underdoped to overdoped regimes, with no significant change in the DOS shape [7,9,10]. The temperature dependence is also unconventional: The gap does not vanish at the critical temperature and a pseudogap persists at T > T c [7,9,[12][13][14][15]. Finally, a low temperature pseudogap remains when the superconducting order is destroyed, within the vortex core [18], or due to disorder [6]. All these features are difficult to explain with a BCS-type theory.In this Letter we report our new low-temperature STS data on YBCO thin films. We observe strongly pronounced peak-dip-hump structures and a significant state density at zero bias. With previous data on BSCCO, our observations suggest a common mechanism for these features, linked to the superconducting state in cuprates. In order to clarify this effect, we propose a new quasiparticle DOS based on an energy-dependent gap function. A particular form for this function is inferred from the data and has, in addition to d-wave symmetry, a single minimum at a characteristic energy near the gap value. Using such a simple ap...