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Associated with each measurable parameter in a physical system is a quantum mechanical operator. Now although not explicitly a time operator the Hamiltonian operator generates the time evolution of the wavefunction in the form H*(Psi)=i*hbar(d/dt)*(Psi), where Psi is a function of both space and time.
Also I don't believe that in the formulation of quantum mechanics (QM) time appears as a parameter, not as a dynamical variable. Also, if time were an operator what would be the eigenvalues and eigenvectors of such an operator?
Note:A dynamical time operator has been proposed in relativistic quantum mechanics.
A paper I found on the topic is;
Zhi-Yong Wang and Cai-Dong Xiong , "Relativistic free-motion time-of-arrival", J. Phys. A: Math. Theor. 40 1987 - 1905(2007)
What else can I help you with?
What is dynamical quantities in quantum mechanics?
In quantum mechanics, dynamical quantities are properties of a physical system that can change with time. These include observables such as position, momentum, energy, and angular momentum, which are represented by operators in the mathematical formalism of quantum mechanics. The study of these dynamical quantities helps describe the evolution of quantum systems over time.
What did Erwin Schrodinger discover in 1930?
Erwin Schrödinger formulated the famous Schrödinger equation in 1926, which is a fundamental equation in quantum mechanics describing how the quantum state of a physical system changes in time. In 1935, he proposed the thought experiment known as "Schrödinger's cat" to illustrate the concept of superposition in quantum mechanics.
What is quantum mechanics?
Quantum mechanics is the mathematical description of matter on an atomic and subatomic scale. It is focused around the wavefunction of a system. Wave functions contain all information about the system such as: momentum, position, angular momentum, energy, etc. This information can only be known by its respective probability distributions. The basis of quantum mechanics in the wave mechanics formulation is the Schrodinger equation, which has two forms: the time-dependent and the time-independent.Quantum mechanics is a branch of mechanics concerned with mathematical modelling of the interaction and motion of subatomic particles.
What is true relativity or quantum mechanics?
Einstein's work on the Photoelectric effect, which won him the Nobel prize in 1921 was a bulwark of Quantum Mechanics. Einstein went off in another direction because of his inate suspicion that Quantum Mechanics has severe internal difficulties. Quantum Mechanics and Relativity have not yet been reconciled--but they are moving together slowly. Quantum Gravity seems to be key to the issue and may be resolved by String Theory.
What are compatible observable in quantum mechanics?
Two operators that are also observables, which means that they correspond to some physically measurable quantity. Compatible observables are two or more such operators that can be measured at the same time. Position and momentum are an example of Incompatible observables, since one can only know either the position or the momentum of an object to 100% accuracy.
What is the significance of using the time ordering operator in quantum mechanics?
The time ordering operator in quantum mechanics is significant because it helps to properly order and calculate the sequence of events in a quantum system. It ensures that the correct chronological order of operations is maintained, which is crucial for accurately predicting and understanding the behavior of particles and systems at the quantum level.
What is the role of the time evolution operator in quantum mechanics when dealing with a time-dependent Hamiltonian?
The time evolution operator in quantum mechanics is used to describe how a quantum system changes over time when the Hamiltonian, which represents the total energy of the system, is time-dependent. It helps to predict the state of the system at any future time based on its initial state and the time-dependent Hamiltonian.
What is the role of the momentum translation operator in quantum mechanics?
The momentum translation operator in quantum mechanics is responsible for shifting the wave function of a particle in space, representing how the particle's momentum changes over time. It helps describe the behavior of particles in terms of their momentum and position in a quantum system.
What is the significance of the unitary operator in quantum mechanics and how does it impact the evolution of quantum systems?
The unitary operator in quantum mechanics is significant because it represents transformations that preserve the probabilities of quantum states. It impacts the evolution of quantum systems by ensuring that the total probability of all possible outcomes remains constant over time, leading to reversible and deterministic quantum dynamics.
Can you make momentum operator non self adjoint?
No, the momentum operator in quantum mechanics must be self-adjoint in order to ensure that it generates unitary time evolution and that the associated probability distribution is conserved. Making the momentum operator not self-adjoint would lead to inconsistencies with the fundamental principles of quantum mechanics.
What is the proof of the Schrdinger equation?
The proof of the Schrdinger equation involves using mathematical principles and techniques to derive the equation that describes the behavior of quantum systems. It is a fundamental equation in quantum mechanics that describes how the wave function of a system evolves over time. The proof typically involves applying the principles of quantum mechanics, such as the Hamiltonian operator and the wave function, to derive the time-dependent Schrdinger equation.
What is the significance of the quantum recurrence theorem in the field of quantum mechanics?
The quantum recurrence theorem is significant in quantum mechanics because it shows that a quantum system will eventually return to its initial state after a certain amount of time. This theorem helps researchers understand the behavior of quantum systems over time and has implications for various applications in quantum physics.
What is the significance of the von Neumann equation in the field of quantum mechanics?
The von Neumann equation is important in quantum mechanics because it describes how a quantum system evolves over time. It helps us understand the behavior of particles at the quantum level and is crucial for predicting and analyzing quantum phenomena.
What are the applications of exponentials of operators in quantum mechanics?
Exponentials of operators in quantum mechanics are used to describe the time evolution of quantum systems. They are important in solving the Schrdinger equation and understanding how quantum states change over time. These exponential operators help calculate probabilities, predict outcomes of measurements, and model the behavior of particles in quantum systems.
What is the significance of the time derivative of the expectation value of position in quantum mechanics?
The time derivative of the expectation value of position in quantum mechanics represents the rate of change of the average position of a particle over time. This quantity is important because it helps us understand how the position of a particle evolves in a quantum system.
What is dynamical quantities in quantum mechanics?
In quantum mechanics, dynamical quantities are properties of a physical system that can change with time. These include observables such as position, momentum, energy, and angular momentum, which are represented by operators in the mathematical formalism of quantum mechanics. The study of these dynamical quantities helps describe the evolution of quantum systems over time.
How does the concept of imaginary time evolution contribute to our understanding of quantum mechanics?
The concept of imaginary time evolution in quantum mechanics helps us understand the behavior of particles at very small scales. It allows us to mathematically describe how particles move and interact in a way that is consistent with the principles of quantum mechanics. This concept helps us make predictions about the behavior of particles in complex systems and provides a framework for understanding the underlying principles of quantum mechanics.
