Solving the Schrodinger Eq: Time Dependency & System Dynamics

In summary, the Schrodinger equation is a fundamental equation in quantum mechanics that describes the evolution of a quantum system over time. It is important because it allows us to understand and predict the behavior of particles at the microscopic level, which is crucial for many areas of science. There are two forms of the equation - the time-dependent and time-independent - which describe different scenarios and have different solutions. The factors that affect the solution to the Schrodinger equation include the potential energy of the system, initial conditions, and energy. It has many real-world applications in fields such as computer chip design, drug development, and quantum technologies. However, it also has limitations, such as its limited applicability to larger systems and its inability to fully explain the
  • #1
saravanan13
56
0
In quantum mechanics, time independent Schrodinger equation gives dynamics of system.
How do one claim that this equation is evolution of a system? Since dynamics need time dependency. How do one explain this discrepancy?
Thanks in well advance...
 
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  • #2
I believe the wave equation gives the probability density function of the electron's position in it's orbit and not the dynamics (movement) of the electron. We have a quantum mechanics forum here. Why don't you ask about the wave equation there.
 

1. What is the Schrodinger equation and why is it important?

The Schrodinger equation is a fundamental equation in quantum mechanics that describes the evolution of a quantum system over time. It is important because it allows us to understand and predict the behavior of particles at the microscopic level, which is crucial for many areas of science such as chemistry, materials science, and quantum computing.

2. What is the difference between the time-dependent and time-independent Schrodinger equation?

The time-dependent Schrodinger equation describes the time evolution of a quantum system when its energy is not constant, while the time-independent Schrodinger equation describes the behavior of a system with a fixed energy. The time-dependent equation is more complex and requires a numerical solution, while the time-independent equation can be solved analytically for simple systems.

3. What factors affect the solution to the Schrodinger equation?

The solution to the Schrodinger equation is influenced by several factors, including the potential energy of the system, the initial conditions of the system, and the energy of the system. Other factors such as external forces or interactions with other particles can also affect the solution.

4. How is the Schrodinger equation used in real-world applications?

The Schrodinger equation is used in a wide range of real-world applications, including computer chip design, pharmaceutical drug development, and material science. It is also the basis for many quantum technologies, such as quantum cryptography and quantum computing.

5. What are the limitations of the Schrodinger equation?

The Schrodinger equation is limited in its applicability to small-scale systems and cannot fully explain the behavior of larger objects. It also does not take into account the effects of relativity, gravity, and other forces that may be important in certain situations. Additionally, the equation is based on probabilistic principles and cannot predict the exact behavior of individual particles, only the overall behavior of a system.

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