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ello! I'm working on quantum mechanics, specifically angular momentum. In class we derived these ladder operators (first picture). So for my homework I'm asked to solve for Lx and Ly in terms of L- and L+ . So I did that and the second picture is what I got. So I'm realising I'm confused by the |ℓ,m> . So we're given a finite number value for ℓ and m. would I just plug in those values and multiply by a 2x1 vector [ l,m]? ([l,m] is supposed to be a vector)

ello! I'm working on quantum mechanics, specifically angular momentum. In class we derived these ladder operators (first picture). So for my homework I'm asked to solve for Lx and Ly in terms of L- and L+ . So I did that and the second picture is what I got. So I'm realising I'm confused by the |ℓ,m> . So we're given a finite number value for ℓ and m. would I just plug in those values and multiply by a 2x1 vector [ l,m]? ([l,m] is supposed to be a vector)

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Hello! I'm working on quantum mechanics, specifically angular momentum. In class we derived these ladder operators (first picture). So for my homework I'm asked to solve for Lx and Ly in terms of L- and L+ . So I did that and the second picture is what I got. So I'm realising I'm confused by the |ℓ,m> . So we're given a finite number value for ℓ and m. would I just plug in those values and multiply by a 2x1 vector [ l,m]?

([l,m] is supposed to be a vector)

Up (X, E) CAN BE SOLVED Up(x, t) 2 WI F.S. Z basin (1) e 2 b₁ = I | -2² NITY [F(x)-(l₂; (x,0)] Sin (²²) dx
Transcribed Image Text:Up (X, E) CAN BE SOLVED Up(x, t) 2 WI F.S. Z basin (1) e 2 b₁ = I | -2² NITY [F(x)-(l₂; (x,0)] Sin (²²) dx
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so like this?

21 \th | Lx|l₁m> = 1/2 √ (+1)-m(m+1) | l, m²) +th | ec^«i)-m(m_r/himar) - +(+-+)²] Lx|l=2₁m=1)=¹₂ √2(211)-1(1+1)' + √2(2+1)-|(1-1) h 1/2 [ 14² + √6²] = 1/2 [ 2+16] * [1.5 ×10²³ 5/5 गड 2 2
Transcribed Image Text:21 \th | Lx|l₁m> = 1/2 √ (+1)-m(m+1) | l, m²) +th | ec^«i)-m(m_r/himar) - +(+-+)²] Lx|l=2₁m=1)=¹₂ √2(211)-1(1+1)' + √2(2+1)-|(1-1) h 1/2 [ 14² + √6²] = 1/2 [ 2+16] * [1.5 ×10²³ 5/5 गड 2 2
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