Normalized function and minimum energy

In summary, a normalized function is a mathematical function where the values are scaled to fit within a specific range. This is achieved by dividing each value by the maximum value in the function. Minimum energy is the point at which a function has the lowest possible output value and is used to determine the most stable state of a system. Normalized functions help to identify the minimum energy point by scaling the values and are commonly used in various fields of science and engineering, as well as in machine learning and data analysis.
  • #1
satach
3
0
please prove this:

<Ψ|[tex]H\overline{^}[/tex]|Ψ>[tex]\geq[/tex]E0
function |Ψ> is normalized.

prompt: (expand function |Ψ> in the eigenbasis of H operator, count average and use ortonormality of the H base)

exercise 5.2.2 , p.163 , "principles of quantum mechanics" Shankar
 
Last edited:
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  • #2
Have you tried using the hint? What did you get after writing |ψ> in the energy basis?
 
  • #3
no, i didn't try , because i don't know how to start :D
 
  • #4
Do you know what an eingenstate is?
 
  • #5
in polish language is sometnihg like : expand |Ψ> in base of self functions of H ...
 

1. What is a normalized function?

A normalized function is a mathematical function where the values of the function are scaled to fit within a specific range. This is usually done to make the function easier to work with and interpret.

2. How is a function normalized?

A function is normalized by dividing each value in the function by the maximum value in the function. This ensures that the values of the function are within the range of 0 to 1.

3. What is the significance of minimum energy in a function?

Minimum energy is the point at which a function has the lowest possible energy or output value. It is used to determine the most stable or optimal state of a system.

4. How are normalized functions and minimum energy related?

Normalized functions help to identify the minimum energy point in a function by scaling the values to be within a specific range. This makes it easier to determine the minimum energy and understand the behavior of the function.

5. What are some real-world applications of normalized functions and minimum energy?

Normalized functions and minimum energy are used in various fields of science and engineering, such as physics, chemistry, and biology, to understand and analyze complex systems. They are also commonly used in machine learning and data analysis to process and interpret data.

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