குவாண்டத்தின் "குவா குவா"
குவண்டம் கணித விரிப்பில்
எப்படி பிரசவிக்கப்படுகிறது.
அருமையான விளக்கங்கள்
அமைந்த திரைப்படம் இது.
இருட்டு சினிமாவில்
உங்கள் அறிவின் வில் அம்புகள்
உடைந்து நொறுங்கி விடும்.
இந்த திரைச்சித்திரம்
உங்கள் அறிவின் பொங்குமாங்கடல்
கொப்பளித்து
அறிவின் இன்பத்தை
அலை அலையாய்க் காட்டும்.
காண்க.
களிப்புறுக.
________________________________________
இ பரமசிவன்
1: Why linear algebra? | Maths of Quantum Mechanics (youtube.com)
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how liner algebra is a tool for Quantum Mechanics?
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Linear algebra is a fundamental tool in quantum mechanics for several reasons:
State Representation: In quantum mechanics, the state of a system is represented by a vector in a complex vector space called a Hilbert space. These vectors, often referred to as “kets” (e.g.,
∣
ψ
⟩
∣ψ⟩
), encapsulate all the information about the quantum state1.
Operators and Observables: Physical quantities, such as momentum and energy, are represented by linear operators acting on these state vectors. For example, the Hamiltonian operator represents the total energy of the system. These operators are often matrices when expressed in a finite-dimensional basis1.
Eigenvalues and Eigenvectors: The possible outcomes of measuring a physical quantity are given by the eigenvalues of the corresponding operator. The state of the system immediately after the measurement is the eigenvector associated with the measured eigenvalue2.
Superposition Principle: Quantum states can be added together to form new states, a property known as superposition. This is a direct consequence of the linearity of the Schrödinger equation, which governs the evolution of quantum states3.
Unitary Evolution: The time evolution of a quantum state is described by a unitary operator, which preserves the inner product (and hence the probability) in the Hilbert space. This ensures that the total probability remains 1 over time4.
Inner Product and Probability: The inner product in Hilbert space, often denoted as
⟨
ϕ
∣
ψ
⟩
⟨ϕ∣ψ⟩
, gives the probability amplitude for transitioning from state
∣
ψ
⟩
∣ψ⟩
to state
∣
ϕ
⟩
∣ϕ⟩
. The modulus squared of this inner product gives the actual probability2.
These aspects make linear algebra indispensable for formulating and solving problems in quantum mechanics. If you have any specific questions or need further details on any of these points, feel free to ask!
1: University of Virginia - Linear Algebra for Quantum Mechanics 2: Quick Reference Guide to Linear Algebra in Quantum Mechanics 3: Physics LibreTexts - Linear Algebra 4: SpringerLink - Linear Algebra and Quantum Mechanics
Learn more
1
galileo.phys.virginia.edu
2
quantum.lvc.edu
3
bing.com
4
phys.libretexts.org
5
link.springer.com
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Can you explain more about eigenvalues and eigenvectors?
How does entanglement relate to linear algebra in quantum mechanics?
What are some common matrix representations of quantum operators?
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