What’s Orthogonal Set in quantum mechanics? And Write its mathematical formula
What’s Orthogonal Set in quantum mechanics? And Write its mathematical formula
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What’s Orthogonal Set in quantum mechanics ? And Write its mathematical formula
![**Orthogonal Set**
\[ \int_{-\infty}^{\infty} \psi_m(x) \psi_n(x) dx = 0, \quad m \neq n \]
(4.24)
**IN OTHER WORDS**
In mathematics, two functions \( f \) and \( g \) are called orthogonal if their inner product \( \langle f, g \rangle \) is zero for \( f \neq g \).
\[ \langle f, g \rangle = \int f(x)^* g(x) \, dx \]
This explanation highlights the concept of orthogonality in mathematical functions. The integral of the product of two orthogonal functions over their domain is zero, indicating that they do not influence each other within that space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3e671be-5699-41c7-ad14-09ef8165fba8%2Fd669c7b1-cb11-41f9-9330-92752103e689%2Fxspw2l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Orthogonal Set**
\[ \int_{-\infty}^{\infty} \psi_m(x) \psi_n(x) dx = 0, \quad m \neq n \]
(4.24)
**IN OTHER WORDS**
In mathematics, two functions \( f \) and \( g \) are called orthogonal if their inner product \( \langle f, g \rangle \) is zero for \( f \neq g \).
\[ \langle f, g \rangle = \int f(x)^* g(x) \, dx \]
This explanation highlights the concept of orthogonality in mathematical functions. The integral of the product of two orthogonal functions over their domain is zero, indicating that they do not influence each other within that space.
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