In quantum mechanics, various quantities can be measured depending on the physical system and the observables associated with it. Observables are properties of a quantum system that can be measured, and each observable corresponds to a physical quantity. Here are some common quantities that can be measured in quantum mechanics:
Position: The measurement of the position of a particle in space is a fundamental quantity in quantum mechanics. It is associated with the position operator, and the measurement provides information about the spatial location of the particle.
Momentum: Momentum is another fundamental quantity that can be measured in quantum mechanics. The momentum operator corresponds to the observable of momentum, and its measurement provides information about the particle's momentum, including both magnitude and direction.
Energy: Energy is a crucial quantity in quantum mechanics. Depending on the system, different types of energy can be measured, such as kinetic energy, potential energy, or total energy. The energy observable corresponds to the energy operator, and measurements provide information about the energy states of the system.
Spin: Spin is an intrinsic property of particles in quantum mechanics. It is associated with the angular momentum of a particle, even in the absence of actual physical rotation. Spin measurements reveal the orientation and magnitude of the particle's spin.
Electric Charge: In quantum mechanics, electric charge is a measurable quantity associated with particles that carry an electric charge. Measurements of electric charge provide information about the amount of charge carried by a particle.
Probability and Amplitude: Quantum mechanics is fundamentally probabilistic. Probabilities and probability amplitudes play a central role in measuring outcomes and predicting the behavior of quantum systems. Measurement outcomes are often expressed as probabilities or probability amplitudes for specific states or observables.
These are just a few examples of the quantities that can be measured in quantum mechanics. There are numerous other observables and corresponding physical quantities that depend on the specific system being studied, such as angular momentum, polarization, particle number, and more. The measurement process in quantum mechanics involves extracting information about these quantities through appropriate measurement operators and analyzing the measurement outcomes.