No, according to our current understanding of quantum mechanics, an electron does not physically rotate like a classical spinning object. The concept of electron "rotation" or "spin" in quantum mechanics is quite different from the macroscopic notion of rotational motion.
Electron spin is an intrinsic property of the electron and is often referred to as an intrinsic angular momentum. It is a fundamental characteristic of elementary particles and is not related to any physical spinning motion. Instead, electron spin is described mathematically as a quantum mechanical property that has no direct classical analogue.
In quantum mechanics, particles such as electrons are described by wave functions, which are mathematical functions that represent the probability distribution of finding the particle in different states. Electron spin is one of the properties described by the wave function.
Spin is quantized, meaning it can only take certain discrete values. For electrons, the spin is quantized as ½, which means the magnitude of the spin angular momentum is equal to ½ times Planck's constant divided by 2π. The spin of an electron can have two possible orientations: spin-up and spin-down.
While the term "spin" may evoke the idea of physical rotation, it is important to note that electron spin is not related to the electron physically rotating on its axis. It is a fundamental property of particles that cannot be directly visualized in classical terms.
The concept of electron spin is crucial for understanding many phenomena in quantum mechanics and is an essential ingredient in the mathematical formalism of the theory. However, its physical interpretation goes beyond our classical intuitions and requires a quantum mechanical understanding.