# Analyse Fonctionnelle. Une introduction pour physiciens by N. Boccara

By N. Boccara

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Temperature nearing absolute zero) it is still supposed to have a non-zero energy value (Fig. 3). Fig. 3 Nature of wavefunctions and corresponding probabilities for the harmonic oscillator problem (Courtesy Wikimedia Commons. This is an edited version: original ﬁle © Alan McC, distributed under the creative commons license) 20 A. ÞÀ1=2 Hn ðqÞeÀq 2 =2 ð52Þ Interestingly there exists a small non-zero part of the wavefunction beyond the potential barrier. This tail of the wavefunction outside the bound system represents a probability that a particle may have a non-zero probability of existing beyond the conﬁning potential, which is the basic concept of quantum mechanical tunneling.

This concept is unique to quantum physics as classically the lowest possible energy of a harmonic oscillator should be zero. e. temperature nearing absolute zero) it is still supposed to have a non-zero energy value (Fig. 3). Fig. 3 Nature of wavefunctions and corresponding probabilities for the harmonic oscillator problem (Courtesy Wikimedia Commons. This is an edited version: original ﬁle © Alan McC, distributed under the creative commons license) 20 A. ÞÀ1=2 Hn ðqÞeÀq 2 =2 ð52Þ Interestingly there exists a small non-zero part of the wavefunction beyond the potential barrier.

Being a layered material, atomically thin layers of MoS2 can be obtained by standard processes such as micromechanical cleavage (scotch tape mechanical exfoliation) and liquid exfoliation. The process of obtaining ultrathin layers from bulk MoS2 by mechanical peeling off had been reported way back in 1965 by Frindt. While in 1986 Joensen, Frindt, and Roy Morrison reported a novel process of intercalation of 2H-MoS2 powder with lithium, followed by an interaction with water and ultrasonication, yielding monolayer MoS2 [24–47].