## (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

Vector

Ket Basis Bra Basis Orthogonality

Normalization ? &amp; ? 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 + ? ? ? &amp; ? 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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This question was answered on: Jan 30, 2021

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STATUS

QUALITY

Approved

Jan 30, 2021

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