Born's rule, which is a fundamental principle in quantum mechanics, provides a way to calculate the probability of finding a quantum object in a particular state when measured. However, it is not the sole factor in determining the probability of quantum tunneling through a potential barrier.
Quantum tunneling refers to the phenomenon where a quantum particle can pass through a potential barrier that would be classically impossible to cross. The probability of tunneling depends on various factors, including the properties of the particle, the shape and height of the barrier, and the specific details of the quantum system.
The mass of the particle is indeed one of the factors that influences the probability of tunneling. In quantum mechanics, the behavior of particles is described by wavefunctions, and the dynamics of these wavefunctions are governed by the Schrödinger equation. When a particle encounters a potential barrier, the Schrödinger equation determines how the wavefunction evolves in space and time.
The mass of the particle is a parameter in the Schrödinger equation and affects the wavelength associated with the particle's wavefunction. Heavier particles have shorter wavelengths, which means they have a higher momentum and tend to be less likely to tunnel through a potential barrier. Conversely, lighter particles have longer wavelengths, allowing them to exhibit more pronounced quantum effects, including a higher probability of tunneling.
However, it's important to note that the mass of the particle is not the only determining factor. The shape and height of the potential barrier, as well as the energy of the particle relative to the barrier, also play significant roles. The specific calculation of tunneling probabilities typically involves solving the Schrödinger equation for the system under consideration, taking into account all relevant parameters and boundary conditions.
In summary, while Born's rule is a fundamental principle for calculating probabilities in quantum mechanics, the calculation of tunneling probabilities through a potential barrier involves considering additional factors such as the mass of the particle, the properties of the barrier, and the specific details of the quantum system.