Yes, conservation laws are indeed obeyed in quantum mechanics. Conservation laws are fundamental principles in physics that state that certain quantities, such as energy, momentum, and angular momentum, are conserved over time in isolated systems.
In quantum mechanics, conservation laws are upheld through the application of specific mathematical operators known as "operators of observables." These operators represent physical quantities, and their conservation is reflected in the behavior of quantum systems.
For example, in quantum mechanics, energy conservation is represented by the time-independence of the total energy operator, known as the Hamiltonian. This operator describes the total energy of a quantum system, including its kinetic energy and potential energy. The time-independence of the Hamiltonian implies that the total energy of an isolated quantum system is conserved over time.
Similarly, momentum conservation is represented by the translational invariance of the system, meaning that if a quantum system is invariant under translations in space, its total momentum is conserved.
Angular momentum conservation is related to the rotational invariance of a system. If a quantum system is invariant under rotations in space, its total angular momentum is conserved.
It's important to note that while conservation laws hold true in quantum mechanics, the specific behaviors and interactions of quantum systems can sometimes differ from classical expectations. Quantum entanglement, for example, allows for correlations between particles that can exhibit non-local behavior, challenging classical intuitions. Nonetheless, conservation laws remain foundational principles in quantum mechanics and are upheld in accordance with the mathematical formalism of the theory.