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Joker93
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What parts of Classical Mechanics must someone know before studying Quantum Mechanics in order to understand the former in all its glory?
Thank you
Thank you
Adam Landos said:What parts of Classical Mechanics must someone know before studying Quantum Mechanics in order to understand the former in all its glory?
Is there a pathway for easily getting the idea behind the things that you mentioned?bhobba said:For a really good understanding the Hamiltonian and Lagranian formalism. I like Landau's beautiful book that emphasises what is also very important in QM - symmetry:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20
Thanks
Bill
Adam Landos said:Is there a pathway for easily getting the idea behind the things that you mentioned?
The former or the latter?Adam Landos said:What parts of Classical Mechanics must someone know before studying Quantum Mechanics in order to understand the former in all its glory?
Oh no, i meant the latter!A. Neumaier said:The former or the latter?
If the former, you need some of all parts of classical mechanics, otherwise you only have part of its glory.
If the latter, does quantum field theory belong to its glory, as far as you are concerned?
Not very much: The Hamiltonian approach to classical dynamics, free motion, the notion of momentum and angular momentum, the 2-body problem. Also useful are the basics about classical waves and the basics of geometric optics.Adam Landos said:What must someone know as far as Classical Mechanics are concerned in order to fully understand undergraduate Quantum Mechanics?
Could you tell me what kind of linear ordinary differential equations must one know before taking a first QM course? Thanks for the reply by the wayA. Neumaier said:Not very much: The Hamiltonian approach to classical dynamics, free motion, the notion of momentum and angular momentum, the 2-body problem. Also useful are the basics about classical waves and the basics of geometric optics.
Far more important is that you have a good command of linear algebra and know how to solve linear ordinary differential equations.
At least:Adam Landos said:what kind of linear ordinary differential equations must one know
Classical mechanics is a theory that describes the motion of macroscopic objects, while quantum mechanics is a theory that describes the behavior of microscopic particles. Classical mechanics follows deterministic laws, while quantum mechanics is probabilistic in nature.
The key principles of quantum mechanics include superposition, where a particle can exist in multiple states simultaneously, and uncertainty, where it is impossible to know both the position and momentum of a particle at the same time. It also includes the concept of wave-particle duality, where particles can exhibit both wave-like and particle-like behavior.
The development of quantum mechanics revolutionized our understanding of the universe by challenging classical notions of determinism and causality. It also led to the discovery of new phenomena, such as quantum entanglement and the observer effect, which have implications for our understanding of reality.
Quantum mechanics has numerous practical applications, including in the development of advanced technologies such as transistors, lasers, and computer chips. It also plays a crucial role in fields such as chemistry, materials science, and cryptography.
Quantum mechanics has connections to other branches of science, such as relativity, through the study of quantum field theory. It also has implications for the study of biology, as quantum effects have been observed in biological systems. Additionally, quantum mechanics plays a role in the development of theories that seek to unify all of the fundamental forces in nature.