Yes, quantum tunneling can occur even if the wavelength of a particle or entity is smaller than the width of the potential barrier. The phenomenon of quantum tunneling allows particles to pass through barriers that would be classically impossible to surmount.
In quantum mechanics, the behavior of particles is described by wave functions, which are related to the probability distribution of finding a particle at a particular location. When a particle encounters a potential barrier, such as a step or a wall, there is a probability that it can tunnel through the barrier and appear on the other side, even if classically it does not possess enough energy to overcome the barrier.
The probability of tunneling depends on various factors, including the width and shape of the barrier, the energy of the particle, and the wavelength associated with it. Although it is true that a smaller wavelength implies a higher momentum and, in classical terms, greater difficulty in penetrating the barrier, quantum mechanics allows for the possibility of tunneling even in these cases.
The wave nature of particles allows them to extend and interfere with themselves spatially. As a result, there is always a non-zero probability of finding the particle on the other side of the barrier, even if its wavelength is smaller than the barrier's width. The wave function associated with the particle can penetrate the barrier due to this spatial extension and interference, allowing for the phenomenon of quantum tunneling.
It's important to note that the probability of tunneling decreases as the barrier width increases or the particle's wavelength decreases. However, the effect is not entirely eliminated. Quantum tunneling has been observed in various physical systems, including electron tunneling in solid-state devices and alpha particle decay in nuclear physics, among others.
In summary, quantum tunneling can occur even if the wavelength of a particle or entity is smaller than the width of the potential barrier. The wave nature of particles allows them to exhibit probabilistic behavior, enabling them to penetrate and pass through barriers that would be classically impassable.