How Do You Derive the Schrödinger Equation from Classical Expressions?

In summary, the Schrodinger equation is a fundamental equation in quantum mechanics that describes the evolution of a quantum mechanical system over time. It was derived by combining classical mechanics and wave mechanics and is based on the principle of conservation of energy. This equation has revolutionized the field of quantum mechanics and is used to make predictions about the behavior and properties of quantum systems. It can be solved using various techniques and has applications in fields such as atomic and molecular physics, condensed matter physics, and quantum chemistry. It is also used in the development of technologies such as lasers, transistors, and superconductors.
  • #1
PhysicalProof
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Homework Statement



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Homework Equations



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This is what I'm trying to obtain, in terms of the elements in the question. Assuming that these 'x' values are 'z'.

The Attempt at a Solution



I'm not really understanding what it is being asked here. Do I just substitute the value of V(z) into obtain the expression? Any advice is appreciated!
 
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  • #2
Anyone have an idea? :(
 
  • #3
I'm thinking that I have to somehow convert that classical expression of V into quantum mechanical terms with operators. Does that sound right?
 

FAQ: How Do You Derive the Schrödinger Equation from Classical Expressions?

What is the Schrodinger equation?

The Schrodinger equation is a mathematical equation that describes the evolution of a quantum mechanical system over time. It is a fundamental equation in quantum mechanics and is used to determine the wave function of a system, which contains all the information about the system's physical properties.

How is the Schrodinger equation derived?

The Schrodinger equation was developed by Austrian physicist Erwin Schrodinger in 1926. It was derived by combining the concepts of classical mechanics and wave mechanics, and it is based on the principle of conservation of energy.

What is the significance of the Schrodinger equation?

The Schrodinger equation revolutionized the field of quantum mechanics and is considered one of the most important equations in physics. It allows scientists to make predictions about the behavior and properties of quantum systems, such as atoms and molecules.

How is the Schrodinger equation solved?

The Schrodinger equation is a complex mathematical equation and can be solved using various techniques, such as numerical methods or analytical methods. The solution to the equation provides the wave function of the system, which can then be used to calculate physical properties of the system.

What are the applications of the Schrodinger equation?

The Schrodinger equation has numerous applications in different fields, such as atomic and molecular physics, condensed matter physics, and quantum chemistry. It is also used in the development of technologies such as lasers, transistors, and superconductors.

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