The value of $\tau$ for an electron in a double square well depends on the specific parameters of the well, such as the well width and depth. This quantity is typically used to describe the average time it takes for an electron to transition between energy levels in the well.
The calculation of $\tau$ involves solving the Schrödinger equation for the energy levels of the electron in the double square well. The value of $\tau$ can then be determined using the equation $\tau = \frac{\hbar}{\Delta E}$, where $\hbar$ is the reduced Planck's constant and $\Delta E$ is the energy difference between the energy levels.
The value of $\tau$ is affected by the width and depth of the well, as well as the shape of the potential barrier between the two wells. Additionally, the mass of the electron and the temperature of the system can also influence the value of $\tau$.
As the width and depth of the well change, so does the value of $\tau$. A wider and deeper well will typically result in a longer $\tau$, as the electron has a greater distance to travel between energy levels. Similarly, a higher potential barrier between the wells can also increase the value of $\tau$.
The value of $\tau$ is an important measure of the time it takes for an electron to transition between energy levels in a double square well. This quantity is often used in the study of quantum mechanics and can provide valuable insights into the behavior of electrons in confined systems.