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(solution) A need a discussion post about explaining what difficulties you


A need a discussion post about explaining what difficulties you have when it comes to unit vector notation and it's equivalent bra-ket notation.

(100+ words, thoughtful and on topic). Original text 


Word Bra-ket Vector |? Adjoint

 

Vector

 

Ket Basis Bra Basis Orthogonality

 

Normalization ? & ? Vectors

 

? ?| ? ? = ? + ? ? |2? ? ?2| ? |1? Components

 

(Real) Inner Product

 

(Real) 0

 

? ?

 

1 (1 ? ? ? ?1|1? (1 ? ? ? ?|? = ? ?1| + ?2|?? |1? + |2??

 

= 2 ?1|1? + ?1|2?

 

+ ?2|1? + 2 ?2|2?

 

2 ?1|? = ?1|? |1? + |2?? = ?1|1? + ?1|2?

 

= ?2|? = ?2|? |1? + |2?? = ?2|1? + ?2|2?

 

= ?|? = ? ?1| + ?2??? |1? + |2??

 

= ?1|1? + ?1|0?

 

+ ?0|1? + ?0|0?

 

= + (1 ? ? ? ? ? ? = ? ? + ?? ? ? ? + ??

 

= 2 ? ? ? + ? ? ?

 

+ ? ? ? + 2 ? ? ?

 

= 2 + ? ) 1

 

? ?

 

0 ? ?1|2? = 2 + ( ? ? ?1| Arrows ? ? ? = ? + ? ?2|2? Length

 

(Real) Matrix 2 (0

 

( ? ? ? = ? ? ? ? + ?? = ? ? ? + ? ? ?

 

= ? ? ? = ? ? + ?? ? ? ? + ??

 

= ? ? ? + ? ? ?

 

+ ? ? ? + ? ? ?

 

= + (0

 

( 1) 0

 

0) ? ? = 0

 

1

 

1

 

0) ? ? = 1

 

0

 

0

 

1) ? ? = 1

 

1 ) ? ? = 2 + 2 (1 ? ? ? = ? ? ? ? + ?? = ? ? ? + ? ? ?

 

= (0 0) 0) ? ? = 1) ? ? = ) ? ? = + Word

 

Length

 

(Complex) Components

 

(Complex) Inner Product

 

(Complex) Bra-ket

 

?|? = ? ? ?1| + ? ?2|?? |1? + |2??

 

= ? ?1|1? + ? ?1|2?

 

+ ? ?2|1? + ? ?2|2? = ? + ? = | |2 + ? ? ? & ? Vectors 2 Matrix ( ? ?1|? = ?1|? |1? + |2?? = ?1|1? + ?1|2?

 

= (1 ?2|? = ?2|? |1? + |2?? = ?2|1? + ?2|2?

 

= ?|? = ? ? ?1| + ? ?2|?? |1? + |2??

 

= ? ?1|1? + ? ?1|2?

 

+ ? ?2|1? + ? ?2|2?

 

= ? + ? 2 ? ) ? ? = | |2 + ? ? (0

 

( ? 0) ? ? = 1) ? ? = ? ) ? ? = ? + ? Arrows

 


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