Is Hamiltonian Mechanics Essential for Studying Quantum Mechanics?

In summary, the conversation revolves around the topic of studying quantum mechanics and whether a knowledge of Hamiltonian and Lagrangian mechanics is necessary for a thorough understanding of QM. Some suggest that books like Marion and Arya's provide a good introduction to these concepts, while others suggest that Landau's book is a must-read. However, it is agreed upon that having a strong background in classical mechanics can greatly aid in understanding QM. A book recommendation is also made for Variational Principles in Dynamics and Quantum Theory by Yourgrau and Mandelstam.
  • #1
veejay
39
0
hello all,

i'm an EE student,and I've recently started studying quantum mechanics.
most textbooks start with schrodinger's equation directly but a few others (like say Liboff) start with the concept of hamiltonian from hamiltonian mechanics.
is a knowledge of the same i.e hamiltonian/lagrangian mechanics essential for a thorough study of QM?
if yes, could someone suggest a good, easy-to-understand text for the former?
i tried referring a few books but they require knowledge of variational calculus.
(i kinda feel the whole process frustrating, spending so much time on this chain of one book to other, ending up doing very little useful work)

thanks.
 
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  • #2
a lot of people knock the newest edition of Marion, but i like its intro to calculus of variations. The book is Classical Dynamics of particles and systems by Marion, Thornton. Its chapter 6, 7, 8 that you're interested in. I also like Arya's book on classical mechanics. I am sure everybody is going to suggest Landau.
 
  • #3
ytoruno said:
a lot of people knock the newest edition of Marion, but i like its intro to calculus of variations. The book is Classical Dynamics of particles and systems by Marion, Thornton. Its chapter 6, 7, 8 that you're interested in. I also like Arya's book on classical mechanics. I am sure everybody is going to suggest Landau.

Actually I agree with you on Marion & Thornton. In particular, the derivation of Lagrangian and Hamiltonian is nice. I think Goldstein is often written with great clarity. To answer the other question, I do think having a solid background in CM will give you a better understanding of QM.
 
  • #4
Variational Principles in Dynamics and Quantum Theory
by Yourgrau and Mandelstam might be interesting. The approach is more historical.
 

FAQ: Is Hamiltonian Mechanics Essential for Studying Quantum Mechanics?

What is Hamiltonian mechanics?

Hamiltonian mechanics is a mathematical framework used to study the motion of particles and systems in classical mechanics. It was developed by Irish physicist William Rowan Hamilton in the 19th century and is based on the principle of least action.

How is Hamiltonian mechanics different from other approaches in classical mechanics?

Unlike other approaches, such as Lagrangian mechanics, Hamiltonian mechanics focuses on the position and momentum of particles rather than their position and velocity. It also uses a different set of equations, known as Hamilton's equations, to describe the motion of particles.

What is the Hamiltonian function?

The Hamiltonian function, denoted by H, is a mathematical function that represents the total energy of a system in Hamiltonian mechanics. It is defined as the sum of the kinetic and potential energies of the particles in the system.

How is the Hamiltonian function used in Hamiltonian mechanics?

In Hamiltonian mechanics, the Hamiltonian function is used to derive the equations of motion for a system. These equations, known as Hamilton's equations, describe how the position and momentum of particles change over time.

What are some applications of Hamiltonian mechanics?

Hamiltonian mechanics has a wide range of applications in physics, engineering, and other fields. It is commonly used in studying the motion of celestial bodies, such as planets and satellites, as well as in the design of control systems for mechanical and electrical systems.

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