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𝑹𝒐𝒍𝒍𝒊𝒏𝒈 𝒄𝒊𝒓𝒄𝒖𝒍𝒂𝒓 𝒅𝒊𝒔𝒌 𝒐𝒏 𝒂𝒏 𝒊𝒏𝒄𝒍𝒊𝒏𝒆𝒅 𝒑𝒍𝒂𝒏𝒆 || 𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝒎𝒐𝒕𝒊𝒐𝒏 𝒃𝒚 𝑳𝒂𝒈𝒓𝒂𝒏𝒈𝒆 𝒎𝒆𝒕𝒉𝒐𝒅
𝑴𝒆𝒓𝒈𝒊𝒏𝒈 𝒕𝒉𝒆 𝑴𝒖𝒍𝒕𝒊𝒑𝒍𝒆 𝑮𝒓𝒂𝒑𝒉𝒔 𝒃𝒚 𝑼𝒔𝒊𝒏𝒈 𝑶𝒓𝒊𝒈𝒊𝒏 𝑺𝒐𝒇𝒕𝒘𝒂𝒓𝒆
𝑷𝒍𝒐𝒕𝒕𝒊𝒏𝒈 𝒕𝒉𝒆 𝑹𝒆𝒇𝒊𝒏𝒆𝒅 𝑿𝑹𝑫 𝑫𝒂𝒕𝒂 (𝒓𝒆𝒇𝒊𝒏𝒆𝒅 𝒃𝒚 𝑭𝒖𝒍𝒍 𝒑𝒓𝒐𝒐𝒇 𝑺𝒖𝒊𝒕𝒆 𝑺𝒐𝒇𝒕𝒘𝒂𝒓𝒆 𝒑𝒂𝒄𝒌𝒂𝒈𝒆) 𝒃𝒚 𝑶𝒓𝒊𝒈𝒊𝒏 𝑺𝒐𝒇𝒕𝒘𝒂𝒓𝒆
𝑫𝒆𝒄𝒐𝒏𝒗𝒐𝒍𝒖𝒕𝒊𝒐𝒏 𝒐𝒇 𝑭𝒆 𝒔𝒑𝒆𝒄𝒕𝒓𝒖𝒎 𝒃𝒚 𝒖𝒔𝒊𝒏𝒈 𝒐𝒓𝒊𝒈𝒊𝒏-8.5 𝒔𝒐𝒇𝒕𝒘𝒂𝒓𝒆 𝒄𝒐𝒏𝒔𝒊𝒅𝒆𝒓𝒊𝒏𝒈 𝑮𝒂𝒖𝒔𝒔𝒊𝒂𝒏 𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏
𝑳𝒆𝒄𝒕 10: 𝑴𝒊𝒔𝒄𝒆𝒍𝒍𝒂𝒏𝒆𝒐𝒖𝒔 𝑸𝒖𝒆𝒔𝒕𝒊𝒐𝒏𝒔 𝒐𝒏 𝑮𝒂𝒎𝒎𝒂 [ Ґ (𝒏) ] 𝒂𝒏𝒅 𝑩𝒆𝒕𝒂 [β (𝒑 , 𝒒)] 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏
𝑳𝒆𝒄𝒕 09: 𝑫𝒊𝒔𝒄𝒖𝒔𝒔𝒊𝒐𝒏 𝒐𝒇 𝑰𝒎𝒑𝒐𝒓𝒕𝒂𝒏𝒕 𝑸𝒖𝒆𝒔𝒕𝒊𝒐𝒏𝒔 𝒐𝒏 𝑩𝒆𝒕𝒂 (𝜷) 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏 [𝑷𝒂𝒓𝒕-02]
𝑳𝒆𝒄𝒕 8: 𝑫𝒊𝒔𝒄𝒖𝒔𝒔𝒊𝒐𝒏 𝒐𝒇 𝑰𝒎𝒑𝒐𝒓𝒕𝒂𝒏𝒕 𝑸𝒖𝒆𝒔𝒕𝒊𝒐𝒏𝒔 𝒐𝒏 𝑩𝒆𝒕𝒂 (𝜷) 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏 [𝑷𝒂𝒓𝒕-01]
𝑳𝒆𝒄𝒕 07: 𝑫𝒆𝒇𝒊𝒏𝒊𝒕𝒊𝒐𝒏, 𝑶𝒕𝒉𝒆𝒓 𝑭𝒐𝒓𝒎𝒔 𝒐𝒇 𝑩𝒆𝒕𝒂 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏 𝒂𝒏𝒅 𝑷𝒓𝒐𝒑𝒆𝒓𝒕𝒊𝒆𝒔 𝒐𝒇 𝑩𝒆𝒕𝒂 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏
𝑳𝒆𝒄𝒕 06: 𝑫𝒊𝒔𝒄𝒖𝒔𝒔𝒊𝒐𝒏: 𝒐𝒇 𝑰𝒎𝒑𝒐𝒓𝒕𝒂𝒏𝒕 𝑸𝒖𝒆𝒔𝒕𝒊𝒐𝒏𝒔 𝒐𝒏 𝑮𝒂𝒎𝒎𝒂 (𝚪) 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏 [𝑷𝒂𝒓𝒕-02]
𝑳𝒆𝒄𝒕 04: 𝑬𝒗𝒂𝒍𝒖𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝑮𝒂𝒎𝒎𝒂 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏 𝒉𝒂𝒗𝒊𝒏𝒈 +𝒗𝒆 𝒂𝒏𝒅 –𝒗𝒆 𝑭𝒓𝒂𝒄𝒕𝒊𝒐𝒏𝒔
𝑳𝒆𝒄𝒕 5: 𝑫𝒊𝒔𝒄𝒖𝒔𝒔𝒊𝒐𝒏 𝒐𝒇 𝑰𝒎𝒑𝒐𝒓𝒕𝒂𝒏𝒕 𝑸𝒖𝒆𝒔𝒕𝒊𝒐𝒏𝒔 𝒐𝒏 𝑮𝒂𝒎𝒎𝒂 (𝚪) 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏 [𝑷𝒂𝒓𝒕-01]
𝑳𝒆𝒄𝒕- 03: 𝑰𝒎𝒑𝒐𝒓𝒕𝒂𝒏𝒕 𝑷𝒓𝒐𝒑𝒆𝒓𝒕𝒊𝒆𝒔 𝒐𝒇 𝑮𝒂𝒎𝒎𝒂 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏
Expectation value of momentum in coordinate and momentum space
Numerical on Laplace Transform of Derivatives and Integrals
𝐅𝐨𝐮𝐫𝐢𝐞𝐫 𝐓𝐫𝐚𝐧𝐬𝐟𝐨𝐫𝐦 𝐨𝐟 𝟏𝐃 𝐆𝐚𝐮𝐬𝐬𝐢𝐚𝐧 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧
