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𝜢

𝜌 = βˆ’π‘–

ℏ𝐻, 𝜌 + πΏπ‘›πœŒπΏ

†𝑛 βˆ’

1

2𝐿†𝑛𝐿𝑛, 𝜌

8

𝑛=1

𝛼 = 2 πœ€ = 0.1

𝑃 πœ™βˆ’ =1

2πœ‹ π‘’π‘–πœ™βˆ’(π‘šβˆ’π‘›) 𝑛, π‘˜ βˆ’ 𝑛|𝜌|π‘š, π‘˜ βˆ’ π‘š

∞

π‘˜=max (𝑛,π‘š)

∞

π‘š=0

∞

𝑛=0

𝑺 = πŸπ… 𝑷 π“βˆ’ π’Žπ’‚π’™ βˆ’ 𝟏

𝐿1 = π‘π‘Žβ€ sin πœ‘ π‘Žπ‘Žβ€ 

π‘Žπ‘Žβ€ 

𝐿2 = 𝑁 cos πœ‘ π‘Žπ‘Žβ€ 

𝐿3 = 𝜈 + 1π‘Ž

𝐿4 = πœˆπ‘Žβ€ 

𝐿5 = 𝑁𝑏†sin πœ‘ 𝑏𝑏†

𝑏𝑏†

𝐿6 = 𝑁 cos πœ‘ 𝑏𝑏†

𝐿7 = 𝜈 + 1𝑏

𝐿8 = πœˆπ‘β€ 

𝐿1 = π‘π‘Žβ€ sin πœ‘ π‘Žπ‘Žβ€ 

π‘Žπ‘Žβ€ 

𝐿2 = 𝑁 cos πœ‘ π‘Žπ‘Žβ€ 

𝐿3 = 𝜈 + 1π‘Ž

𝐿4 = πœˆπ‘Žβ€ 

𝐿5 = 𝑁𝑏†sin πœ‘ 𝑏𝑏†

𝑏𝑏†

𝐿6 = 𝑁 cos πœ‘ 𝑏𝑏†

𝐿7 = 𝜈 + 1𝑏

𝐿8 = πœˆπ‘β€ 

𝐻 = βˆ† π‘Žβ€ π‘Ž βˆ’ 𝑏†𝑏

𝜌 = βˆ’π‘–

ℏ𝐻, 𝜌 + πΏπ‘›πœŒπΏ

†𝑛 βˆ’

1

2𝐿†𝑛𝐿𝑛, 𝜌

8

𝑛=0

π‘³πŸŽ = 𝜺 𝒂 βˆ’ 𝒃

𝐻 = βˆ† π‘Žβ€ π‘Ž βˆ’ 𝑏†𝑏 + 𝜺 𝒂†𝒃 + 𝒃†𝒂

π’ͺ

𝑁 = 5

πœ€ = 0.01

o

o

o

𝑁 = 5 𝛼 = 2

𝑁 = 5 𝛼 = 2

πœΊπ‚βˆ†

𝝋 = 𝑡/𝜢

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