Math Problem Statement
bra a1 phi1 + a2 phi2 ket b1 psi1 b2 psi2 expand this
Solution
To expand the expression , we can distribute and use the properties of inner products in quantum mechanics.
Here’s the step-by-step expansion:
- Distribute the terms:
Here’s a breakdown of each term:
- : This is the inner product of and , weighted by and .
- : This is the inner product of and , weighted by and .
- : This is the inner product of and , weighted by and .
- : This is the inner product of and , weighted by and .
Final expanded form:
Would you like me to explain any specific part further, or would you like to proceed with another related concept?
Related questions:
- What is the physical significance of the inner product ?
- How do you calculate inner products in a basis of vectors?
- What happens if and are orthogonal?
- How can you use the above expansion to simplify a matrix element in quantum mechanics?
- Can you apply this expansion to calculate probabilities in quantum systems?
Tip: Always keep in mind the complex conjugate when dealing with inner products involving coefficients like or .
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Math Problem Analysis
Mathematical Concepts
Quantum Mechanics
Inner Products
Linear Algebra
Formulas
Inner product expansion formula
Distributive property
Theorems
Properties of inner products in quantum mechanics
Suitable Grade Level
Undergraduate
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