Need suggestion about Laplacian and Hamilton Operator

In summary, the Laplacian operator is a mathematical operator used in vector calculus to describe the rate of change of a scalar field or the divergence of a vector field. It is often denoted by the symbol ∇² or Δ and is defined as the sum of the second-order partial derivatives of a function with respect to its spatial coordinates. On the other hand, the Hamilton operator, also known as the Hamiltonian operator, is a mathematical operator used in quantum mechanics to describe the energy of a quantum system. It is denoted by the symbol Ĥ and is defined as the sum of the kinetic and potential energy operators of the system. While the Laplacian operator is commonly used in fields such as fluid dynamics, electromagnetism,
  • #1
haohan
2
0
Hi,

Someone has some suggestion about self-study book about "Laplacian" and "Hamilton Operator".

Thanks
 
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  • #2
It depends on the degree of detail and mathematical formalism that you want.

"Quantum Mechanics" by David J. Griffiths. Not as good as his book on electrodynamics, but complete and very didactil. Ideal for self-study.

When I studied Physics, we used "Quantum Mechanics" by Cohen-Tannoudji et al (it seems that it is no longer in print). Very formal but easy to read and to understand.
 
  • #3
Gonfer, thanks for your reply. I will try these two and see whether they help me.
 

What is the Laplacian operator?

The Laplacian operator is a mathematical operator used in vector calculus to describe the rate of change of a scalar field or the divergence of a vector field. It is often denoted by the symbol ∇² or Δ and is defined as the sum of the second-order partial derivatives of a function with respect to its spatial coordinates.

What is the Hamilton operator?

The Hamilton operator, also known as the Hamiltonian operator, is a mathematical operator used in quantum mechanics to describe the energy of a quantum system. It is denoted by the symbol Ĥ and is defined as the sum of the kinetic and potential energy operators of the system.

What is the difference between the Laplacian and Hamilton operator?

The Laplacian operator is used to describe the rate of change of a scalar field or the divergence of a vector field, while the Hamilton operator is used to describe the energy of a quantum system. The two operators are fundamentally different in their applications and cannot be used interchangeably.

What are some real-life applications of the Laplacian and Hamilton operator?

The Laplacian operator is commonly used in fields such as fluid dynamics, electromagnetism, and image processing. It can be used to model the flow of fluids, calculate electric or magnetic fields, and enhance images. The Hamilton operator is primarily used in quantum mechanics to solve Schrödinger's equation and predict the behavior of quantum systems.

How do I use the Laplacian and Hamilton operator in my research?

The Laplacian and Hamilton operator can be used in various research fields, depending on your specific area of study. To use these operators, you will need a strong understanding of vector calculus and quantum mechanics. It is recommended to consult with a mentor or expert in your field for guidance on how to apply these operators in your research.

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