The concept of coherence and quantum tunneling applies to different physical systems, so it is not directly meaningful to compare the probabilities of quantum tunneling for a molecule in a coherent state versus an electron. Let's break it down:
Coherent States: In quantum mechanics, a coherent state is a special type of quantum state that exhibits certain classical-like properties. It is typically associated with systems that can be described by harmonic oscillators, such as a quantum harmonic oscillator or certain types of electromagnetic fields. Coherent states have well-defined amplitudes and phases and are often characterized by their classical-like behavior.
Quantum Tunneling: Quantum tunneling refers to the phenomenon where a particle can pass through a potential barrier even though its energy is lower than the height of the barrier. It arises from the probabilistic nature of quantum mechanics and the wave-like properties of particles. Quantum tunneling is observed in various systems, such as electrons tunneling through potential barriers in solid-state devices or alpha particles escaping from atomic nuclei.
In the case of coherent states, they are typically associated with macroscopic systems or collective states of many particles. For example, a coherent state of a molecule could describe its vibrational or rotational motion. The concept of quantum tunneling is more commonly applied to individual particles, such as electrons, where their wave-like nature allows them to tunnel through potential barriers.
While it is possible to have coherent superposition states of molecules, the concept of quantum tunneling in the context of a molecule in a coherent state is not as straightforward as for individual particles like electrons. The behavior of molecules is influenced by a complex interplay of various factors, including their structure, interactions, and environmental effects.
In summary, the notion of quantum tunneling and the probabilities associated with it are more commonly discussed in the context of particles like electrons, rather than in the context of molecules in coherent states.